Answer
The solutions are $6$ and $-6$.
Work Step by Step
$ z^{2}-7=29\qquad$ ...add $7$ to each side.
$ z^{2}=29+7\qquad$ ...simplify.
$ z^{2}=36\qquad$ ...take square roots of each side.
$\sqrt{z^{2}}=\sqrt{36}\qquad$ ...simplify.
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$z=\pm 6$
