Question

Solve by completing the square:

2x² + 2x − 12 = 0

Answer 1

Given:

2x² + 2x − 12 = 0

x² + x − 6 = 0

x² + x = 6

Complete the square:

Coefficient of x = 1

Half = `1/2`

Square = `(1/2)^2 = 1/4`

`x^2 + x + 1/4 = 6 + 1/4 =25/4`

`(x + 1/2)^2 = 25/4`

Take square root of both sides

`x + 1/2 = +-5/2`

Case 1:

`x = -1/2 + 5/2 = 4/2 = 2`

Case 2:

`x = -1/2 -5/2 = -6/2 = -3`

x = 2 or x = −3​