Answer
$x=\{ -5, 0 \}$
Work Step by Step
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solution/s of the given quadratic equation, $
x^2+5x=0
,$ is/are
\begin{array}{l}\require{cancel}
x=\dfrac{-5\pm\sqrt{5^2-4(1)(0)}}{2(1)}
\\\\
x=\dfrac{-5\pm\sqrt{25-0}}{2}
\\\\
x=\dfrac{-5\pm\sqrt{25}}{2}
\\\\
x=\dfrac{-5\pm5}{2}
\\\\
x=\{ -5, 0 \}
.\end{array}