Answer
The solution set is $\left\{-\frac{5}{9}, \frac{5}{9}\right\}$.
Work Step by Step
Add $-25$ to both sides to find:
$81x^2-25=0
\\(9x)^2-5^2=0$
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 find:
$(9x-5)(9x+5)=0$
Equate each factor to 0 then solve each equation to find:
$9x-5=0 \text{ or } 9x+5=0\\
9x=5 \text{ or } 9x=-5
\\x=\frac{5}{9} \text{ or } x=-\frac{5}{9}$
The solution set is $\left\{-\frac{5}{9}, \frac{5}{9}\right\}$.
