Answer
The solutions are $1+\sqrt{2}$ and $1-\sqrt{2}$
Work Step by Step
$ 4(x-1)^{2}=8\qquad$ ...divide each side with $4$.
$(x-1)^{2}=2\qquad$ ...take square roots of each side.
$\sqrt{(x-1)^{2}}=\sqrt{2}\qquad$ ...simplify.
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$ x-1=\pm\sqrt{2}\qquad$ ...add $1$ to each side.
$ x-1+1=\pm\sqrt{2}+1\qquad$ ...simplify.
$x=1\pm\sqrt{2}$
