Quadratic equation can be solved using factorization method, completing the square method and quadratic formula method. In this module we will study the ‘completing the square method’.
Solve the quadratic equation, using the ‘completing the square’ method. Follow these steps:
- Step 1. Make the coefficient of x2 unity (i.e., 1)
- Step 2. Take the coefficient of x, now divide it by 2, now take the square of this value, the result obtained should be added and subtract in the original equation to maintain the original value of equation.
- Step 3. Take the x2 term, the x term and the constant (that you just added and subtracted) to form the perfect square. Using the identity (a+b)² = a²+b²+2ab
- Step 4. Take the remaining term on the right hand side
- Step 5. Take the square rot on both the side.
- Step 6. Do not forget to take both positive and negative sign. Because square of both (+x) and (-x) is (x2)
- Step 7. Simplify the equation; transfer the constant term to right hand, taking positive and negative sign one by one.
- Step 8. In this way you will get two values of quadratic equation
Let us take a numerical example to understand this method in a better way:
Let us take the original quadratic equation to be 2x²-7x+6=0
Now make the coefficient of x2 unity (i.e., 1)
The equation will become
The equation simplify to
Now let us take the coefficient of x, that is now take half of it, , now do the square of this value, it would become , now add and subtract in the above equation
Now rearrange the equation as
Now since is equivalent to because of identity
Now our equation simplifies t
Now transfer the constant term on right hand side
Now taking the square root on both the side
Now there are two cases
Case 1: taking positive sign
Case 2: taking negative sign
To build a command on this method, try to practice as many questions as possible.
Try following algebra homework
After solving question 3 you will realize, you face square root of a negative number. It is called iota and it I beyond the concept of normal algebra. T is dealt in greater detail in complex number and complex algebra.
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