Question

How do you solve `8x^2+32x-24` by completing the square?

Answer 1

`x = -2 +sqrt 7, -2 - sqrt 7`

Explanation:

`8 x^2 + 32 x - 24 =0`

reduce coefficient `x^2` to 1 by dividing with `8`
`x^2 +4x -3 = 0`

consider coefficient of `x` and divide by 2 then make a parentesis and square them, then square the number in parentesis and deduct it in the equation.
`(x + 2)^2 - (2)^2 - 3 = 0`
`(x + 2)^2 - 4 - 3 = 0`
`(x + 2)^2 - 7 = 0`
`(x + 2)^2 = 7`
`(x + 2) = +-sqrt 7`
`x = -2 +-sqrt 7`

`x = -2 +sqrt 7, -2 - sqrt 7`