Answer
{$-\frac{3}{7},\frac{5}{7}$}
Work Step by Step
Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain:
Step 1: $2(7x-1)^{2}+5=37$
Step 2: $2(7x-1)^{2}=37-5$
Step 3: $2(7x-1)^{2}=32$
Step 4: $(7x-1)^{2}=16$
Step 5: $7x-1=\pm \sqrt {16}$
Step 6: $7x-1=\pm 4$
Step 7: $7x-1=4$ or $7x-1=-4$
Step 8: $7x=4+1$ or $7x=-4+1$
Step 9: $7x=5$ or $7x=-3$
Step 10: $x=\frac{5}{7}$ or $x=-\frac{3}{7}$
The solution set is {$-\frac{3}{7},\frac{5}{7}$}.
