Question

Solve by completing the square:

2x² + 5x − 6 = 0

Answer 1

Given:

2x² + 5x − 6 = 0

Move the constant to the right-hand side

2x² + 5x = 6

Divide the entire equation by 2:

`x^2 + 5/2x = 3`

Complete the square

Coefficient of x = `5/2`

Half = `5/4`

Square = `(5/4)^2 = 25/16`

`x^2 + 5/2x + 25/16 = 3 + 25/16`

`3 = 48/16`

`=> 48/16 + 25/16 = 73/16`

`(x+5/4)^2 = 73/16`

`x + 5/4 = +- sqrt(73/16) = +- sqrt73/4`

`x = -5/4 +- sqrt73/4`

`x = -5/4 = +- sqrt73/4`

`x = (-5+-sqrt73)/4`