Answer
The solutions are $x=9+\sqrt{5}$ or $x=9-\sqrt{5}$
Work Step by Step
$ x^{2}-18x+81=5\qquad$ ...write left side as a binomial squared.($81=9^{2}$)
$(x-9)^{2}=5\qquad$ ...take square roots of each side.
$ x-9=\pm\sqrt{5}\qquad$ ...add $9$ to each side.
$ x-9+9=\pm\sqrt{5}+9\qquad$ ...simplify.
$x=9\pm\sqrt{5}$
$x=9+\sqrt{5}$ or $x=9-\sqrt{5}$
