Answer
The solution set is $\left\{-\frac{6}{7}, \frac{6}{7}\right\}$.
Work Step by Step
Add $-36$ to both sides to obtain:
$49x^2-36=0 (7x)^2-6^2=0$
RECALL:
A difference of two squares can be factored using the formula:
$a^2-b^2=(a-b)(a+b)$
Factor the difference of two squares to obtain:
$(7x-6)(7x+6)=0$
Equate each factor to 0, and then solve each equation to obtain:
$7x-6=0 \text{ or } 7x+6 = 0
\\7x=6 \text{ or } 7x=-6
\\x=\frac{6}{7} \text{ or } x=-\frac{6}{7}$
The solution set is $\left\{-\frac{6}{7}, \frac{6}{7}\right\}$.
