Answer
$x=\left\{ 1 \right\}$
Work Step by Step
Factoring the given equation, $
x^2+1=2x
,$ results to
\begin{array}{l}\require{cancel}
x^2-2x+1=0
\\\\
(x-1)^2=0
\\\\
(x-1)(x-1)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(x-1)(x-1)=0
,$ are
\begin{array}{l}\require{cancel}
x-1=0
\\\\
x=1
,\\\\\text{OR}\\\\
x-1=0
\\\\
x=1
.\end{array}
Hence, $
x=\left\{ 1 \right\}
.$