Question

Solve by completing the square:

4x² + 4√3x + 3 = 0

Answer 1

Given:

4x² + 4√3x + 3 = 0

Divide the whole equation by 4:

`x^2 + sqrt3x + 3/4= 0`

`x^2 + sqrt3x = -3/4`

Complete the square

Coefficient of x = `sqrt3`

Half = `sqrt3/2`

Square = `(sqrt3/2)^2 = 3/4`

`x^2 + sqrt3 x + 3/4 = -3/4 + 3/4 = 0`

`(x+ sqrt3/2)^2 = 0`

Solve for x

`x + sqrt3/2 = 0`

`x = -sqrt3/2`