# How do you solve 16x^2 = 24?

Mar 2, 2018

The answers are $\frac{\sqrt{6}}{2}$ and $- \frac{\sqrt{6}}{2}$.

#### Explanation:

$16 {x}^{2} = 24$

$\frac{16 {x}^{2}}{16} = \frac{24}{16}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{16}}} {x}^{2}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{16}}}} = \frac{24}{16}$

${x}^{2} = \frac{24}{16}$

${x}^{2} = \frac{3}{2}$

$\sqrt{{x}^{2}} = \sqrt{\frac{3}{2}}$

$x = \pm \sqrt{\frac{3}{2}}$

$\textcolor{w h i t e}{x} = \pm \frac{\sqrt{3}}{\sqrt{2}}$

$\textcolor{w h i t e}{x} = \pm \frac{\sqrt{3}}{\sqrt{2}} \textcolor{red}{\cdot \frac{\sqrt{2}}{\sqrt{2}}}$

$\textcolor{w h i t e}{x} = \pm \frac{\sqrt{3} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}}$

$\textcolor{w h i t e}{x} = \pm \frac{\sqrt{3 \cdot 2}}{\sqrt{2 \cdot 2}}$

$\textcolor{w h i t e}{x} = \pm \frac{\sqrt{6}}{\sqrt{4}}$

$\textcolor{w h i t e}{x} = \pm \frac{\sqrt{6}}{2}$