Answer
{$-\frac{5}{3},3$}
Work Step by Step
Using Property 10.1, which states that for any non-negative real number $a$, $(x-b)^{2}=a$ can be written as $x-b=\pm\sqrt a$, we obtain:
Step 1: $(3x-2)^{2}=49$
Step 2: $3x-2=\pm \sqrt {49}$
Step 3: $3x-2=\pm 7$
Step 4: $3x-2=7$ or $3x-2=-7$
Step 5: $3x=7+2$ or $3x=-7+2$
Step 6: $3x=9$ or $3x=-5$
Step 7: $x=3$ or $x=-\frac{5}{3}$
The solution set is {$-\frac{5}{3},3$}.
