#### Answer

$x=\{1, 11\}$

#### Work Step by Step

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}