How to Solve Quadratic Equations within a minute without a Calculator?

A quadratic equation is the branch of algebra which is the important part of mathematics. It includes three important terms as variable, content, and coefficient. Before going to solve the equation without greatest common factor, you need to know some basics about the algebraic expression. The quadratic algebraic equation includes 2nd order degree on the variable. Hence, there are two values you can find for a variable. Consider an example as mx² + nx + p = 0

Here some of the common term as

Variables: Variables are the term whose value varies with constant and coefficient available in the mathematical expressions. Here ‘x’ is the variable in given equation.

Constant: Constant value is the numerical value or number available in the equation which cannot be changed. In the above equation, the ‘p’ is the constant value.

Coefficient: in the term of any algebraic equation, a coefficient is also the numerical value. In the given standard quadratic equation’ and ‘n’ are coefficients.

How to solve the quadratic equation without a calculator?

Consider examples to solve the quadratic equations without using the calculator and formulas.

x² + 5x + 6 = 0

x² – 5x + 6 = 0

x² – 5x – 6 = 0

x² + 5x – 6 = 0

There are four quadratic examples, and it can be solved without the formula method. It is easy when you have great skill in mathematical calculation.

For first equation to solve it- 

x² + 5x + 6 = 0

First, you have to choose the right factor. For this, you have selected the coefficient of x² and constant value. After getting factors, you need to make set where the sum of these is equal to the coefficient of ‘x.’ now divide both the factors by the coefficient of x² . And the most important (+, +) signs make (-,-) in the result.

For above equation, factors are 1 and 6, and 6 can be factored as 2 and 3. The multiplication of 2×3 is equal to 6 and the sum of 2+3 = 5. So we get 2 and 3 as a result.

For second equation

x² – 5x + 6 = 0

We have (-, +) signs on the quadratic equation. The factors are 2 and three as identified above in the expressions. So, the signs provide (+, +) signs on the result. Now the equation provides two values as (3, 2).

For third equation

x² – 5x – 6 = 0

There are (-, -) signs are available which provide (+,-) signs on the result. The factors are 2 and 3 for the above equations. Keep the thing in mind that the first sign is for big numerical value. Now the value of ‘x’ is (3, -2).

For fourth equation

x² + 5x – 6 = 0

In algebra problem there are (+,-) signs which provide (-, +) signs in the result. And the first sign is always for the big numerical value. Now the equation provides (-3, 2) values for ‘x.’ in this method, dividing fractions is a difficult task. Also, you can experience the decimal to fraction and fraction to a decimal operation to make the complex equation simple.

Instead of this short method, the formula can be used.


This is also the easiest method to solve quadratic equations, but some mathematical calculation makes it difficult.


Pick up the Best Method to Solve Quadratic Equation

There are many interesting facts and lessons that you may get to witness in mathematics. You may get to experience some of the best ones in the algebraic portions. Algebra stands to be one of the most important parts of mathematics and has many interesting things for the learners. Quadratic equations being some of the complex algebraic problems, there are many who find some better ways to solve quadratic equations. Equations are not so difficult if you relate the various components in it with something easier. You may see that these are just like the fill in the blocks exercises that you solved in the childhood.

Quadratic Formula
Quadratic Formula

Quadratic Equation – its complete meaning

An equation can be said to be any algebraic expression that is stated in the form of ax²+bx+c = 0

is known as a quadratic equation. Here, a, b, and c are known to be constants, and “x” is the variable. Therefore solving such complex equations may involve some specific methods and essential steps to be performed. These are a bit more complex than linear equations, therefore, you need to move out to advanced learning and solving strategies. There are many different methods that you can use to solve equations like this. There are both advantages and disadvantages related to the use of these methods. Considering these will help you to get the correct answers more easily.

Know the various methods

There are many ways in which you can bring out the correct answers fir the value of “x” in the quadratic equations. Knowing the best one will help you to complete algebra homework on time. Therefore here are the methods used to solve quadratic equations:

Completing the Square: This is usually a process including multiple steps. In this method, the main motive is to convert the quadratic in the form of (x+a)² = b

  • The condition here remains the same,e., and b are constants. This method is the best to give perfect insights of the working of algebra. Also, this method is known to bring the correct answers always which are the advantage of using it. However, the disadvantage with it is the complexity it may involve.
  • Factoring: the factors of any quadratic equations will be said to be (max + r)
    and (nx + t). However, you will be able to find the correct answers only when the solution is an integer. Non integer solutions will not be found with this method which constitutes to its disadvantage. This method can be performed really faster, and it is the advantage with it.

Quadratic Formula: the formula is stated as:  -b±√b²-4ac ⁄ 2a the quadratic formula is designed in a way that it reduces the complex steps that are involved in solving a quadratic. This makes it straightforward which is the advantage. However the technique can turn out to be rote constituting to be the disadvantages.

Thus you can make use of these methods to complete your algebra homework. Though these are a bit complex than linear equations, you can make use of the simplest and the best methods. These will help you to solve quadratic equations and get the correct solutions.

How to Simplify System of Equations

There is a linear and nonlinear system of equations. The latter being a set of simultaneous equations whereby the unknowns appear as variables of a polynomial of degree higher than one in the argument of a function which isn’t a polynomial of degree one. Nonlinear equations are not always easy to deal with. Quadratic equations are examples of nonlinear equations. In short, a system of equations is a set of equations that are dealt with all together at a go.

Since solving these equations isn’t always a walk in the park, some guys decided to come up with a desktop application that simplifies them. They are called softmath, and they are based in the US. They called that app “Algebrator”.

How does algebrator work?

First of all, it can be downloaded through the link that is provided on their webpage As of now, its cost is roughly ten bucks. But, that is bound to change in the next few hours. So if you feel like purchasing it after paying attention to what it does, I would advise you to do that sooner rather than later.

Now, let us dive deep into Algebrator. This solution tackles problems from many math textbooks. It tackles those that are in Trigonometry, Statistics, Pre-Algebra, and College Algebra. Imagine it can solve problems from the following topics; complex numbers, graphing, trigonometry, equations, and inequalities, logarithms, functions, math expressions to name but few. Is that not great? I bet it is.

The app allows the use of wizards interface or WYSIYWG interface (an acronym of What You See Is What You Get interface) to enter problems like “Find a perpendicular line that passes the (x, y) coordinates”.

With this app, you can ask for the explanation of something if you did not get how it arrived at that place. Just like how the teacher shows his or her steps while calculating something, this application will do the same too. That way, it makes sure that you have understood how it some things are done.

When you get the solution, you can export it in MathML format. If you do not mind, you can go ahead and share that solution with your friends or classmates or even everyone. The application has an export function which generates xhtml files which can be easily opened in web browsers like Google Chrome, Mozilla Firefox, Internet Explorer, Microsoft Edge, Safari, Opera and many more.

Who can install this application?

As of now, the app can be installed on Windows PCs or Mac OS laptops.

Do they provide customer support service?

Yes, they do. Softmath provides customer services every week day from 8 o’clock in the morning to 9 o’clock in the evening. They can also be reached through the phone call using the number that they have indicated in their webpage.

If you prefer having a one on one talk, you can get them at their office which is located along Blanco Road in the city of San Antonio in the State of Texas.

Know dividing polynomials with small example to understand better

dividing polynomials

Dividing polynomials is not an easy task as it seems. Sometimes the polynomials equations include higher degree that is why it is difficult to solve it. Basically, the polynomial equation is same as the algebraic or the quadratic equation. But the major difference between both is the algebraic equation does not contain degree on variables, but quadratic includes it. The polynomial equation usually contains same variables in the quadratic form. To better understand consider an example which is suitable-

3a + 2b = 18 algebraic equation

x²+2x+ 8=0 Polynomial equation

When you are dividing polynomials, and then feel some difficulties. Due to lack of knowledge of mathematics operation and the complexity of polynomial; makes it more difficult. The variables include different values that are why it is hard to solve. There is no direct method to solve polynomial equations.

When you are looking for understating the dividing the polynomial consider an example.


This is divided by


The dividing rule is same as we have performed in previous classes. But the variable in dividing polynomials makes complexity in solution.

Take the figure in this form as below



To solve this polynomial determine the degree of both the equation. As shown in the first equation has 3 higher degrees and the second includes one.

In the first step of division, to need to divide first equation by     x²

We take x² because it can eliminate the (x³) from the equation. In a first step, we can eliminate the higher degree than we go to the lower degree.

After division we have,


Now you have to follow the second step in which, the elimination of second-degree performs. Divide the equation with ‘5x’ that can help you to eliminate the term 5x².

Now we have taken 5 with the variable it is done to eliminate both x² and 5 from the equation. After dividing the above equation, you will get,


Now we have eliminated the first and second degree. Now you have to eliminate the variable which includes a single degree. For this purpose, we need to repeat the previous step with different numerical values. Divide the above equation by (x-2) with (-3)’s multiplication. This will help you to eliminate (-3x) from the equation.

After division, you have 0 remnants. So, keep the numbers which are multiplied by the divider. Above we used

x² , 5x and -3

We need to add these results to get the final answer.

Hence the solution of this equation is

x²+5x -3

Basically, it is not difficult to solve the equation, but it needs huge grip in a calculation, division, multiplication and much more. Also, it needs great basic knowledge of mathematics for dividing polynomial. In the current, the polynomial equation is taken to know the intelligence of people. That is why it is used in many competitive exams. It makes the brain exercise perfect and helps to master in a calculation. It is beneficial for us so, we need to practice more and more to understand the division polynomial. After regular practice, you can become a master in it.

You can get Math Help for Various Topics on the Internet

Students have a worry with math, and it becomes difficult for them to solve problems of mathematics. They have difficulty in algebra as well as geometry. They should take the benefit of online math help on the internet. You can use some good online portals that will help you to solve many problems of mathematics. Most of the students can’t solve the various problems of algebra. They can easily solve algebra problems by taking the advantage of the internet. You can get a lot of help on many websites, and you can also do your math homework easily by using a suitable website.

Math Help
Math Help

You can get help on so many topics

Algebra itself is a vast subject. The main topics of these subjects are quadratic equations, linear equations, graphing, sequences, functions, logarithms, complex numbers, matrices, statistics, etc. you can get relevant and useful math help on any of this topic on the web. A good website not only provides you the simple steps to solve any problem of math but also illustrate the topic with proper examples. You can know the rules of any topic as well as its definition. The explanation you get on the web is very informative and helpful for the students.

For example, if you have a query to find the Greatest Common Factor of a number, you can get easy steps to solve it. You can get the definition and theory about this topic. You can choose a suitable solving method from many methods given on a website. You can see the solved examples on the GCF problems. The simplest way to find the GCF of any two numbers is to find the prime factors of both these numbers. Then select all the common factors of both the numbers. Then, evaluate the greatest number from all the common factors of these two numbers. It is the GCF of those two numbers. You can get more methods to solve it on a good online portal.

Take the benefit of solved examples and useful information

You can get a complete list of formulas on any topic. You can also understand any topic by the help of many solved problems. You will get the simplest steps to solve the problems of any topic such as quadratic equations, complex numbers, and much more topics. If students follow these steps, they will get a right solution. Some online portals have advanced software that can solve some mathematical problems online. You can check your answer and can solve the difficult problems by the use of the right software. Thus, you can get very useful math help on a right website easily on the internet.

The Internet is easily accessible to almost every person, and it can be a good platform to learn things. You can learn any topic of algebra using the internet and teach other students. You can solve any problem of your textbook with the help of a good and appropriate website on the internet. You can know how to solve any mathematical problem on the internet. Thus, students can use the internet for getting good math help easily and quickly.

All about Linear and Quadratic Polynomials

Polynomials are algebraic terms which are two or more in numbers. They are also known as expressions and consist of the variable, constants, and coefficient. Besides this, they are of two types i.e. linear and quadratic polynomials plus they can be high degree and low degree. For solving them, you should be used to factoring methods and basic of algebra. So, let’s start our lessons.

How to solve linear polynomial?

At first, you should know how a linear polynomial looks like? In it, you will see variable with exponents one for example 3x+2. Let’s look at the steps for solving it:

  • Sat first you have to set the polynomials in which you have to insert an equal sign in front of it like this 3x+2=0.
  • Many people suggest you isolate terms but why to do that when you can give the answer by just looking at the expression.
  • What you have to do is to separate like terms like shift 2 to the RHS and 3x to LHS. In other change their sides like this, 3x=0-2. Sort out like terms, and with this simple trick, you can obtain the answer quickly.
  • Now, 3x= -2 and now bring three under two as like this x=-2/3.

You should take care of the similar terms, sides, and sign. Guys keep in mind that signs changes when you change the sides of the expression or constants.

How to solve a quadratic equation?

In it, the polynomial is of second degree which means that variables have exponent 2.

Let’ solve.

  • First thing guys, always make sure that the polynomial must be in right order. In other words, higher degree expression should come first or their degree must be in order.
  • Now, guys find out the factors of 20 plus you should use these factors in a way that it will give (-8) and will also give 20 when multiplied together.
  • You have to multiply one with 20 as the coefficient of is one plus for finding factors, it is an important to step.
  • 2, 2 and 5 are its factors so you should simplify it in a way mentioned above. Let’s multiply 5 and 2 to get 10 and leave two alone. It is also known as a grouping of factors.
  • Now, write four expressions like this

    . Now, divided them from the middle and formed two groups. Do like this: x(x+10)-2(x+10)=0 . Here we have taken x and two as common terms.

  • Also, while splinting into expressions, make sure you write signs right. The two group of binomials are visible to you i.e. ( x+10) and (x-2).
  • Now, you have to solve it like linear polynomials and get an answer(x=-10,x=2). Again, while using zero in the polynomial, change sings

Algebra is a very easy topic, and polynomials are like basics for other topics like linear or quadratic equations. You can solve another example of polynomials by the steps describe above plus understand properly how to group factors in it?

Make it Fun: Help your Children with any Kind of Algebra Problem

algebra problem

Mathematics has been one of the most interesting subjects in the complete studies series. Algebra is the most important and interesting components of this interesting subject. There are many people who love to solve an algebra problem. However, there are many who are scared of mathematics too. Therefore people usually look out for ways which can make mathematics more interesting for their children. There are many tricks and tips to make it easier to solve various problems in algebra. However, there is more need to make it a fun activity. This will be the best way to induce the interest of your children in mathematics and make them perfectionists.

Algebra and Fun

Here are some excellent tips which will help you to make math absolutely fun for your children. These will be very useful to you, therefore, go through these:

  • Make it a Game: Let you children deal with math not as a subject or a matter of studies but like a game. This will induce their interest in this subject and help them know things in a better way. These days there are many apps and other resources to make math easy and more interesting. Try to involve algebraic identities in some interesting This can be easily done through various board games and non-mathematical tasks.
  • Integrate these into fun activities: Find out the activities that are usually enjoyed by your children. Now blend algebra problem into these games. This will bring your children both knowledge and enjoyment. This is the best way to help you children memorize different rules and identities. Therefore you need to find some best games and combine them with algebraic identities and problems.
  • Make it real and meaningful: Let your children solve such problems for realistic situations. This will provide them with the best practical knowledge and let them learn more and faster.  There may be many situations in the regular life when there is a requirement of arithmetic and algebraic problems to be solved. Children should be assigned this work as this will help them improve their speed and skills.
  • Encourage Mental Math: Teach your children to solve problems and do calculations mentally rather than in writing. This will keep them alert and increase their speed of solving problems. Perfect mental math will lead them towards quick and perfect actions and solutions. Therefore try to take up some time and indulge them in the solving mental problems. These will prove to be the best booster for them.
  • Reward them for better performance: It is good to reward your children when they bring out the answers correctly. These rewards are the best encouragements for your children which will initiate to work even better. Thus there are many ways of making it extremely

The tips mentioned above will help you in the best way to make algebra fun for your children and help them solve any algebra problem perfectly. There are much more ways which can help you however these are enough. Therefore move on and make studies fun for your children.

Do you Struggle Solving Algebraic Equations?

Subtracting Fractions

Not everybody is a fast learner. But that should not be taken to mean that the slow learners won’t understand anything in class. They will, even though after some time. The most important thing is to understand at least one or two things. Imagine having a math tutor or a lecturer or a teacher coming to class, lecturing and then disappearing without you, the student, shooting some questions? You will be loosing a lot if you fail to ask questions. Even then it is understandable that some people hate asking questions in front of their classmates. Especially the shy ones. However, you need not worry anymore because there is a better way of learning algebra besides the one from class. There is a problem-solver called algebrator.


This software package solves algebraic assignments that you have been given by your teacher. It solves any problem from any math textbook that you come across. Be it trigonometry, college algebra, statistics or pre-algebra. This software package costs only ten dollars when you use the link provided in at this website ( This website has been created in two languages i.e. English and Spanish. You can select the language that you are comfortable using.

Any algebraic equations that you can think of can be simplified using this desktop application. It solves Problems like subtracting fractions, solving inequalities and logarithms, matrices, complex numbers, sequences and much more.

It shows the steps it took to arrive at any answer. This can be compared to the way the teacher explains his or her steps she took in order to arrive at the answer shown in the black or whiteboard.

Entering your problems to this package is very easy. It uses the approach of What You See Is What You Get or better known as WYSIWYG interface. This, therefore, means that you can enter problems like “find perpendicular line to another passing through point x”

Once a solution is obtained, you can export it to Math ML format and then share it with the rest. The export function of this application generates xhtml files that can be opened by many browsers.

Surprisingly, this application has an offer for those who would like to order it before midnight of 15th of April 2017. You will get over one thousand problems that have been entered by other users of this application.

Any available customer support?

In case you need some things clarified or anything that relates to algebrator, feel free to send them an email using the address provided on their website ( If you are comfortable making a phone call, they have indicated their contact digits at the same webpage. You can still visit their offices if you do not mind. They are located along Blanco Rd in San Antonio city, the state of Texas in United States of America. Be warned though, their offices are only opened from Monday to Friday and as early as 8 O’clock in the morning and closed late in the evening at exactly 9 o’clock.

Softmath Best for Adding Fractions


Are you having a problem with any mathematics problem, it is high time you gave softmath a try, and it will never disappoint you. This tool is designed to be a problem solver as far as mathematics is concerned. If you are among those students that have an incurable hatred for mathematics, soft math will cure you of that hatred and mathematics will soon become your best subject.  The software can do practically anything in mathematics. It is used in adding fractions, solving groups of the equation and even drawing graphs.  Would you want to simplify or expand a mathematical expression? You can find help with this software. It is the perfect tool everyone having problems with mathematics should have.

Are you having a problem with any GCF or LCM-related problems? You can also get them solved by using this software. It can teach you virtually anything related to mathematics. The software can perform Simplification operation. In this instance, it will accept any mathematical expression you provide and get it simplified. It gets its job done following College Algebra rules, which are the art of the background information the software is built on. It can be used in adding fractions, and it will get it done under few minutes. No more waste of time or waste of energy to get that mathematics problem solved. It will also remove the need for any mental stress from you. It will present the solution in the clearest and most understandable manner imaginable.

Would you rather expand a mathematical expression? You can trust softmath also to get this done for you. All you have to do is to provide an expression, and the software will get it solved in no time at all. However, you must first find out if the expression is expandable before asking the software to expand it for you. For an expression to be expandable, it must contain a product or power of terms. If the expressions are in form of fractions, you can also trust softmath for adding fractions perfectly.  It is designed to work fast, and it will have the answers ready in few minutes.  The solution presented by the software is very easy to understand.

Softmath can perform any Factor operation you present to it too.  As long as the expression is factor-able, the software will not have any problem handling it. Find out if the expression is a sum of terms before you enter it into the software. Once this is settled, the software will get the job done in the twinkle of an eye.  Aside from adding fractions, it can also subtract, multiply and divide fractions.

When solving any Simplification problem, you may not be able to use any of the inequality signs. This is because inequalities and equations need to b solved and not simplified.  You can draw a graph for any equation related to systems, inequalities, and equations using this software.  A valid equation for graph needs to contain the equality or inequality sign for it to be valid. The software is easy to understand, and there is nothing complicated about it at all.

Mixed Fraction Calculator


If 1 bowl of rice is cooked in 2 and a half bowls of water, how much water is required to cook 3 and a half bowls of rice? In real life and the pace at which modern world operates, students need to know how to convert fractions to decimals and vice versa. In today’s real world, fractions less than 1/8 are not generally used except in very specific fields like wood working. If the beginners are familiar with the eights, they are through to most of the calculations they come up in the day to day tasks. Before computers and calculators, 1 or 2 digit fraction calculations were easier than performing computing 3 or more digit decimals. Presently, the practical world demands mathematicians, engineers, and scientists to work with English system fractions. Therefore, to assist these professionals and also beginners or students, mixed fraction calculators nowadays, are available in the form of web applications, desktop software and even as mobile or tablet apps. These calculators offer math calculations with mixed numbers (mixed fractions) allowing to perform operations on fractions, whole numbers, integers, proper fractions and improper fractions. The mixed numbers calculator also has the capability to add, subtract, multiply and divide mixed numbers and fractions.

Generally, the online versions of the calculators handle simple operations on whole numbers, integers, mixed numbers, improper and proper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if the conversion allows.

The Algorithm:

The mixed fraction calculators add mixed number using the adding fractions formula. It includes firstly, conversion of mixed numbers to improper fractions. Then use the algebraic formula i.e. ‘a/b +c/d = (ad+bc) / bd’,  for addition of fractions. The last step involves expression reduction and simplification if possible. Similarly subtracting mixed numbers also involves the conversion of mixed number to an improper fraction, applying the algebraic formula ‘a/b -c/d = (ad-bc) / bd’ and at last simplifying the expression. The multiplication operation also involves the mixed fraction to improper fraction conversion. Then the algebraic formula ‘a/b * c/d = ac / bd’ is employed to multiply fractions, and finally, reduction and simplifications are done if required. Last but not the least, division operation in mixed numbers calculators is performed using the dividing fractions formula. As done in the other three arithmetic operations earlier, the initial step involves mixed fraction to improper fraction conversion. Then the algebraic formula of division of fractions i.e. ‘a/b ÷ c/d = ad / bc’ is used. The final step involves simplification process as previously done. The simplification process performed by the software calculators involves a code that utilizes Euclid’s theorem for reducing fractions.

Real world applications:

Mixed numbers or fractions are used in every walk of life, all round us. For example, for a carpenter the problem could be like while building a wooden house and framing the walls, the outer wall is 30  Feet long, and he wants to put a stud every 1 foot, 6 inches. How many studs would be needed for this particular job? Students at a beginner level are taught these operations by problems that involve the division of cake pieces or pizza slices. That makes it easier for them to proceed towards complex problems.