How do you solve 36 = 4 sqrt(4m^2+5)?

Mar 25, 2018

The two solutions are $m = \pm \sqrt{19}$.

Explanation:

$36 = 4 \sqrt{4 {m}^{2} + 5}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{36}}{4}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{4 \sqrt{4 {m}^{2} + 5}}}{4}}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{36}}{4}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{\textcolor{red}{\cancel{\textcolor{B l a c k}{4}}} \sqrt{4 {m}^{2} + 5}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{36}}{4}} = \sqrt{4 {m}^{2} + 5}$

$9 = \sqrt{4 {m}^{2} + 5}$

${9}^{2} = {\left(\sqrt{4 {m}^{2} + 5}\right)}^{2}$

${9}^{2} = 4 {m}^{2} + 5$

$81 = 4 {m}^{2} + 5$

$76 = 4 {m}^{2}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{76}}{4}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{4 {m}^{2}}}{4}}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{76}}{4}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} {m}^{2}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}}$

$19 = {m}^{2}$

$\pm \sqrt{19} = \sqrt{{m}^{2}}$

$m = \pm \sqrt{19}$

These are the solutions. Hope this helped!