Answer
{$-\frac{2}{5},\frac{4}{5}$}
Work Step by Step
We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain:
Step 1: $(5x-1)^{2}=9$
Step 2: $5x-1=\pm \sqrt {9}$
Step 3: $5x-1=\pm 3$
Step 4: $5x=1\pm 3$
Step 5: $x=\frac{1\pm 3}{5}$
Step 6: $x=\frac{1+ 3}{5}$ or $x=\frac{1- 3}{5}$
Step 7: $x=\frac{4}{5}$ or $x=\frac{-2}{5}$
Therefore, the solution set is {$-\frac{2}{5},\frac{4}{5}$}.
