Answer
$\color{blue}{\left\{-\frac{\sqrt2}{2}, 0, \frac{\sqrt2}{2}\right\}}$
Work Step by Step
Factor out the GCF $x^2$ to obtain:
$$x^2(1-2x^2)=0$$
Use the Zero-Factor Property by equating each factor to zero to obtain:
$x^2=0$ or $1-2x^2=0$
Solve each equation to obtain:
$x^2=0
\\x=\pm \sqrt0
\\x=0$
or
$1-2x^2=0
\\1=2x^2
\\\frac{1}{2}=x^2
\\\pm\sqrt{\frac{1}{2}}=
\\\pm \sqrt{\frac{1\cdot2}{2\cdot2}}=x
\\\pm \frac{\sqrt2}{2}=x$
Thus, the solution set is $\color{blue}{\left\{-\frac{\sqrt2}{2}, 0, \frac{\sqrt2}{2}\right\}}$.
