Question

How do you solve the quadratic equation by completing the square: `x^2+8x-2=0`?

Answer 1

`color(green)(x = sqrt 18 - 4` or `color(green)(x = -sqrt 18 -4`

Explanation:

`x^2 + 8x = 2`

To write the Left Hand Side as a Perfect Square, we add 16 to both sides.

`x^2 + 8x + 16 = 2 + 16`

`x^2 + 2*4*x + 4^2 = 18`

Using the Identity `color(blue)((a+b)^2 = a^2 + 2ab + b^2`, we get
`(x+4)^2 = 18`
`x + 4 = sqrt18` or `x +4 = -sqrt18`
`color(green)(x = sqrt 18 - 4` or `color(green)(x = -sqrt 18 -4`