Chapter 8 - Sections 8.1-8.3 - Integrated Review - Summary on Solving Quadratic Equations - Page 504: 6

$x=\{1, 11\}$

Using the completing the square method, the solutions of the given quadratic equation, $ x^2-12x+11=0 ,$ is \begin{array}{l}\require{cancel} x^2-12x=-11 \\\\ x^2-12x+\left( \dfrac{-12}{2}\right)^2=-11+\left( \dfrac{-12}{2}\right)^2 \\\\ x^2-12x+36=-11+36 \\\\ (x-6)^2=25 \\\\ x-6=\pm\sqrt{25} \\\\ x-6=\pm5 \\\\ x=6\pm5 \\\\ x=\{1, 11\} .\end{array}