Question

Solve by completing the square:

x² + 3x − 8 = 0

Answer 1

Given:

x² + 3x − 8 = 0

Move the constant to the right-hand side

x² + 3x = 8

Complete the square

Coefficient of x = 3

Half = `3/2`

Square = `(3/2)^2 = 9/4`

`x^2 + 3x + 9/4 = 8+9/4`

`8 = 32/4`

`=> 32/4 + 9/4 = 41/4`

`= (x+3/2)^2 = 41/4`

`x + 3/2 = +- sqrt(41/4) = +- sqrt41/2`

`x = -3/2 +- sqrt41/2`

`x = (-3+-sqrt41)/2`