Question

Solve by completing the square:

4x² − 3 = 2x

Answer 1

Given:

4x² − 3 = 2x

Bring all terms to one side

4x² − 2x − 3 = 0

 Divide the entire equation by 4:

`x^2 - 1/2  x - 3/4 = 0`

`x^2 - 1/2 x = 3/4`

Complete the square

Coefficient of x = `-1/2`

Half = `-1/4`

Square = `(1/4)^2 = 1/16`

`x^2 - 1/2x +1/16 = 3/4 + 1/16`

`3/4 = 12/16`

`=> 12/16 + 1/16 = 13/16`

`(x-1/4)^2 = 13/16`

`x - 1/4 = +- sqrt(13/16) = +-sqrt13/4`

`x = 1/4 +- sqrt13/4`

`x = (1+sqrt13)/4 or x = (1-sqrt13)/4`