Answer
The solution set is {$1, -\frac{1}{5}$}.
Work Step by Step
$g(x)=(x-\frac{2}{5})^2, g(x)=\frac{9}{25}$
For $g(x)=(x-\frac{2}{5})^2$, substitute $g(x)$ with $\frac{9}{25}$
$\frac{9}{25} = (x-\frac{2}{5})^2$
Using the Square Root Property $u^2 = d$, then $u = \sqrt d$ or $u = - \sqrt d$.
Thus,
$x-\frac{2}{5} = \sqrt \frac{9}{25}$ or $x-\frac{2}{5} = -\sqrt \frac{9}{25}$
$x = \frac{2}{5}+ \sqrt \frac{9}{25}$ or $x =\frac{2}{5} -\sqrt \frac{9}{25}$
$x = \frac{2}{5} + \frac{3}{5}$ or $x = \frac{2}{5} - \frac{3}{5}$
$x = 1$ or $x = -\frac{1}{5}$
The solution set is {$1, -\frac{1}{5}$}.
