Complete the Square Calculator

A quadratic equation is of the form ax²+ bx + c = 0 and we can solve this equation by various methods. One of the methods to solve a quadratic equation is by ‘Completing the square’. Complete the square calculator is the online tool which can complete the square instantly.

 

Example 1: Solve by completing the square: x² + 6x -7 = 0

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

Add ‘7’ on both sides! ? x²+6x = 7

Now divide the coefficient of ‘x’ by ‘2’? 6/2 = 3

Now square the number got from the previous step ? 3² = 9

Add the above ‘9’ on both sides ? x²+6x+9=7+9 ? x²+6x+9 = 16

Now x²+6x+9 can be factored as (x+3) (x+3) = (x+3)²

(x+3)² = 16 ?x+3 = √16

x+3 = +- 4?x = -3 +-4

x = 1 and x= -7

 

Example 2: Solve by completing the square: x² + 4x – 8 = 0

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

Add ‘8’ on both sides! ? x²+4x = 8

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 = 8+4 ? x²+4x+4 = 12

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

(x+2)² = 12 ?x+2 = √12

 x = -2 + 2√3 and x = x = -2 - 2√3