8.3.4 Finding the Solutions

Compare your answer:

$m=4$ and $m=-4$

$5m^2=80$

$\frac{5m^2}{5}=\frac{80}{5}$

$m^2=16$

$m=\pm \sqrt{16}$

$m=4$ and $m=-4$

Compare your answer:

$m=16$ and $m=-4$

$(m-6{)}^2=100$

$(m-6)=\pm \sqrt{100}$

$m-6=10m-6=-10$

$m=16$ and $m=-4$

Compare your answer:

$y=3$ and $y=-3$

$\begin{array}{ccc}\hfill \frac{2}{3}{y}^2-8& \hfill =\hfill & -2\hfill \\ \hfill \frac{2}{3}{y}^2& \hfill =\hfill & 6\hfill \\ \hfill \frac{3}{2}\left(\frac{2}{3}{y}^2\right)& \hfill =\hfill & \frac{3}{2}\left(6\right)\hfill \\ \hfill y^2& \hfill =\hfill & 9\hfill \\ \hfill y& \hfill =\hfill & \pm \sqrt{9}\hfill \end{array}$
$y=3$ and $y=-3$

Compare your answer:

$x=9$ and $x=-15$

$\begin{array}{ccc}\hfill \frac{1}{6}{(x+3)}^2-8& \hfill =\hfill & 16\hfill \\ \hfill \frac{1}{6}{(x+3)}^2& \hfill =\hfill & 24\hfill \\ \hfill {(x+3)}^2& \hfill =\hfill & 144\hfill \\ \hfill (x+3)& \hfill =\hfill & \pm \sqrt{144}\hfill \end{array}$
$x+3=12x+3=-12$
$x=9$ and $x=-15$