Answer
$x=\{ -4,2 \}$
Work Step by Step
The two numbers whose product is $ac=1(-8)=-8
$ and whose sum is $b=
2
$ are $\{
4,-2
\}$. Using these two numbers to decompose the middle term of the given equation, $
x^2+2x-8=0
,$ results to
\begin{array}{l}\require{cancel}
x^2+4x-2x-8=0
\\\\
(x^2+4x)-(2x+8)=0
\\\\
x(x+4)-2(x+4)=0
\\\\
(x+4)(x-2)=0
.\end{array}
Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x+4=0
\\\\
x=-4
,\\\\\text{OR}\\\\
x-2=0
\\\\
x=2
.\end{array}
Hence, the solutions are $
x=\{ -4,2 \}
.$
