Answer
{$-\frac{13}{5},\frac{1}{5}$}
Work Step by Step
Using Property 10.1, which says that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain:
Step 1: $(5n+6)^{2}=49$
Step 2: $5n+6=\pm \sqrt {49}$
Step 3: $5n+6=\pm 7$
Step 4: $5n+6=7$ or $5n+6=-7$
Step 5: $5n=7-6$ or $5n=-7-6$
Step 6: $5n=1$ or $5n=-13$
Step 7: $n=\frac{1}{5}$ or $n=-\frac{13}{5}$
The solution set is {$-\frac{13}{5},\frac{1}{5}$}.
