Answer
$x=\left\{ 5-\sqrt{3},5+\sqrt{3} \right\}$
Work Step by Step
The left side of the given equation, $
x^2-10x+25=3
,$ is a perfect square trinomial whose factored form is
\begin{array}{l}\require{cancel}
(x-5)^2=3
.\end{array}
Taking the square root of both sides (the Square Root Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x-5=\pm\sqrt{3}
\\\\
x=5\pm\sqrt{3}
.\end{array}
Hence, $
x=\left\{ 5-\sqrt{3},5+\sqrt{3} \right\}
.$
