Answer
$x=5\pm\sqrt{23}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
x^2-10x+2=0
,$ is
\begin{array}{l}\require{cancel}
x^2-10x=-2
\\\\
x^2-10x+ \left( \dfrac{-10}{2} \right)^2=-2+\left( \dfrac{-10}{2} \right)^2
\\\\
x^2-10x+ 25=-2+25
\\\\
(x-5)^2=23
\\\\
x-5=\pm\sqrt{23}
\\\\
x=5\pm\sqrt{23}
.\end{array}