Answer
The solutions are $m=13$ or $m=-11$.
Work Step by Step
$ m^{2}-2m+1=144\qquad$ ...write left side as a binomial squared.
$(m-1)^{2}=144\qquad$ ...take square roots of each side.
$ m-1=\pm 12\qquad$ ...add $1$ to each side.
$ m-1+1=\pm 12+1\qquad$ ...simplify.
$ m=1\pm 12\qquad$ ...write as separate equations.
$m=1+12$ or $ m=1-12\qquad$ ...simplify.
$m=13$ or $m=-11$
