Answer
The solutions are $x=11+\sqrt{13}$ or $x=11-\sqrt{13}$.
Work Step by Step
$ x^{2}-22x+121=13\qquad$ ...write left side as a binomial squared.
($121=11^{2}$)
$(x-11)^{2}=13\qquad$ ...take square roots of each side.
$ x-11=\pm\sqrt{13}\qquad$ ...add $11$ to each side.
$ x-11+11=\pm\sqrt{13}+11\qquad$ ...simplify.
$ x=11\pm\sqrt{13}\qquad$ ...write as separate equations.
$x=11+\sqrt{13}$ or $x=11-\sqrt{13}$
