## Precalculus (6th Edition)

$\color{blue}{\left\{-\frac{\sqrt2}{2}, 0, \frac{\sqrt2}{2}\right\}}$
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 $\color{blue}{\left\{-\frac{\sqrt2}{2}, 0, \frac{\sqrt2}{2}\right\}}$.