Answer
The solution set is $\{\frac{13}{5},\frac{7}{5}\}$.
Work Step by Step
The given expression is
$\Rightarrow 25(x-2)^2=9$
Divide each side by $25$.
$\Rightarrow (x-2)^2=\frac{9}{25}$
$\frac{9}{25}\geq0$ is a nonnegative number.
Use the square root method.
$\Rightarrow x-2=\pm\sqrt {\frac{9}{25}}$
Use $\sqrt {\frac{9}{25}}=\frac{3}{5}$.
$\Rightarrow x-2=\pm\frac{3}{5}$
Add $2$ to each side.
$\Rightarrow x-2+2=\pm\frac{3}{5}+2$
Simplify.
$\Rightarrow x=\pm\frac{3}{5}+2$
The solutions are $x=\frac{3}{5}+2=\frac{3+10}{5}=\frac{13}{5}$ and $x=-\frac{3}{5}+2=\frac{-3+10}{5}=\frac{7}{5}$
Hence, the solution set is $\{\frac{13}{5},\frac{7}{5}\}$.
