Answer
{$-8,0$}
Work Step by Step
Step 1: $x^{2}+8x=0$ can also be written as $x^{2}+8x+0=0$. Comparing $x^{2}=8x+0=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain:
$a=1$, $b=8$ and $c=0$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a,b, and c in the formula, we obtain:
$x=\frac{-(8) \pm \sqrt {(8)^{2}-4(1)(0)}}{2(1)}$
Step 4: $x=\frac{-8 \pm \sqrt {64-0}}{2}$
Step 5: $x=\frac{-8 \pm \sqrt {64}}{2}$
Step 6: $x=\frac{-8 \pm 8}{2}$
Step 7: $x=\frac{-8+8}{2}$ or $x=\frac{-8-8}{2}$
Step 8: $x=\frac{0}{2}$ or $x=\frac{-16}{2}$
Step 9: $x=0$ or $x=-8$
Step 10: Therefore, the solution set is {$-8,0$}.
