x^2 + 4x - 8 = 0
Move constant to right side.
x^2 + 4x = 8
Let's complete the square to find x.
(4/2)^2 = 4
We add 4 to both sides.
x^2 + 4x + 4 = 8 + 4
Factor left side.
(x + 2)(x + 2) = 12
(x + 2)^2 = 12
Take square root on both sides.
sqrt{(x + 2)^2} = sqrt{12}
x + 2 = 2•sqrt{3}
x + 2 = -2•sqrt{3}
Two answers:
x = - 2 + 2•sqrt{3}
And
x = -2 - 2•sqrt{3}
