Completing the Square Calculator

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A quadratic equation is of the form ax2+ bx + c = 0 and it can be solved by different methods. One such method is ‘Completing the square’ method where an equation is made a perfect square by making some changes. Completing the square calculator is an instant tool which can calculate the solution of a quadratic equation.

 

Example 1: Solve by completing the square: 2x2 + 4x - 6 = 0

Divide the entire equation by ‘2’ ? x2+2x-3=0

Check whether the co-efficient of x2 is 1. Yes!

Add ‘3’ on both sides! ? x2+2x=3

Now divide the coefficient of ‘x’ by ‘2’?2/2 = 1

Now square the number got from the previous step?12 = 1

Add the above ‘1’ on both sides ? x2+2x+1=3+1?x2+2x+1 = 4

Now x2+2x+1 can be factored as (x+1) (x+1)=(x+1)2

(x+1)2 = 4 ?x+1 = √4

x+1 = +- 2 ?x = 1 and x= -3

 

Example 2: Solve by completing the square: x2+4x-12=0

Check whether the co-efficient of x2 is 1. Yes!

Add ‘12’ on both sides! ? x2+4x = 12

Now divide the coefficient of ‘x’ by ‘2’? 4/2 = 2

Now square the number got from the previous step ? 22 = 4

Add the above ‘4’ on both sides ? x2+4x+4 = 12+4 ? x2+4x+4 = 16

Now x2 + 4x + 4 can be factored as (x+2) (x+2) = (x+2)2

(x+2)2 = 16 ?x+2 = √16?x+2 = +-4

x=2 and x = -6

 

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