Chapter 8 - Section 8.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 485: 52

$x=5\pm\sqrt{23}$

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}