Answer
$x=\left\{ 8 \right\}$
Work Step by Step
Factoring the given equation, $
64+x^2=16x
,$ results to
\begin{array}{l}\require{cancel}
x^2-16x+64=0
\\\\
(x-8)^2=0
\\\\
(x-8)(x-8)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(x-8)(x-8)=0
,$ are
\begin{array}{l}\require{cancel}
x-8=0
\\\\
x=8
,\\\\\text{OR}\\\\
x-8=0
\\\\
x=8
.\end{array}
Hence, $
x=\left\{ 8 \right\}
.$