Answer
The solutions are $4$ and $6$.
Work Step by Step
$ x^{2}-10x+25=1\qquad$ ...write left side as a binomial squared.$-10x=(-2x)(5)$
$(x-5)^{2}=1\qquad$ ...take square roots of each side.
$ x-5=\pm 1\qquad$ ...add $5$ to each side.
$ x-5+5=\pm 1+5\qquad$ ...simplify.
$ x=5\pm 1\qquad$ ...write as separate equations.
$x=5+1$ or $ x=5-1\qquad$ ...simplify.
$x=6$ or $x=4$
