How do you solve the equation (3x-2/3)^2-2=5/2?

Feb 21, 2018

$x = \frac{2}{9} \pm \frac{\sqrt{2}}{2}$

Explanation:

$\text{add 2 to both sides}$

$\Rightarrow {\left(3 x - \frac{2}{3}\right)}^{2} = \frac{9}{2}$

$\textcolor{b l u e}{\text{take square root of both sides}}$

$\sqrt{{\left(3 x - \frac{2}{3}\right)}^{2}} = \pm \sqrt{\frac{9}{2}} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\Rightarrow 3 x - \frac{2}{3} = \pm \frac{3}{\sqrt{2}} = \pm \frac{3}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3 \sqrt{2}}{2}$

$\text{add "2/3" to both sides}$

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

$\text{divide both sides by 3}$

$\Rightarrow x = \frac{2}{9} \pm \frac{\sqrt{2}}{2} \leftarrow \textcolor{red}{\text{exact values}}$