Answer
$x=\left\{ -5 \right\}$
Work Step by Step
Factoring the given equation, $
0=25+x^2+10x
,$ results to
\begin{array}{l}\require{cancel}
25+x^2+10x=0
\\\\
(x+5)^2=0
\\\\
(x+5)(x+5)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(x+5)(x+5)=0
,$ are
\begin{array}{l}\require{cancel}
x+5=0
\\\\
x=-5
,\\\\\text{OR}\\\\
x+5=0
\\\\
x=-5
.\end{array}
Hence, $
x=\left\{ -5 \right\}
.$