This problem illustrates the logic involved in solving a quadratic equation by completing the square. (This particular equation can also be factored, but it's been chosen so as to keep the arithmetic simple.)

Enter (without the quotation marks) "$==>$" if the left equation implies the right, "$<==$" if the right equation implies the left, "$<==>$" if either equation implies the other, and "$><$" if neither equation implies the other.

$x^2+2x-8 = 0$ $x^2+2x+1 = 9$. (add 9 on both sides).

$x^2+2x+1 = 9$ $(x+1)^2 = 9$. (Apply the binomial formula $x^2+2ax+a^2= (x+a)^2$, with $a=1$, on both sides.)

$x^2+2x+1 = 9$ $x+1=3$. (one possibility).

$x^2+2x+1 = 9$ $x+1=-3$. (the other possibility).
Thus the solutions of $x^2+2x-8 = 0$ are $x=-4$ and $x=2$.