Answer
$x=-5$
Work Step by Step
Using the properties of equality, the given equation, $
x^2+10x=-25
,$ is equivalent to
\begin{align*}
x^2+10x+25=0
\end{align*}
In the equation above, $a=
1
,$ $b=
10
,$ and $c=
25
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}x&=
\dfrac{-10\pm\sqrt{10^2-4(1)(25)}}{2(1)}
\\\\&=
\dfrac{-10\pm\sqrt{100-100}}{2}
\\\\&=
\dfrac{-10\pm\sqrt{0}}{2}
\\\\&=
\dfrac{-10\pm0}{2}
\\\\&=
\dfrac{-10}{2}
\\\\&=
-5
\end{align*}
Hence, the solution is $
x=-5
.$
