Answer
The solutions are $22$ and $2$.
Work Step by Step
$ x^{2}-24x+144=100\qquad$ ...write left side as a binomial squared.($144=12^{2}$)
$(x-12)^{2}=100\qquad$ ...take square roots of each side.
$ x-12=\pm 10\qquad$ ...add $12$ to each side.
$ x-12+12=\pm 10+12\qquad$ ...simplify.
$ x=12\pm 10\qquad$ ...write as separate equations.
$x=12+10$ or $ x=12-10\qquad$ ...simplify.
$x=22$ or $x=2$
