How do you solve the equation 3(x-3)^2+2=26?

Sep 26, 2017

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

Explanation:

$3 {\left(x - 3\right)}^{2} = 26$

$\rightarrow 3 {\left(x - 3\right)}^{2} = 24$

$\rightarrow {\left(x - 3\right)}^{2} = 8$

$\rightarrow {x}^{2} - 6 x + 9 = 8$

$\rightarrow {x}^{2} - 6 x + 1 = 0$

$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \left(1\right) \left(1\right)}}{2 \left(1\right)}$
$\textcolor{w h i t e}{\text{XxXX}} = \frac{6 \pm \sqrt{32}}{2}$
$\textcolor{w h i t e}{\text{XxXX}} = \frac{6 \pm 4 \sqrt{2}}{2}$
$\textcolor{w h i t e}{\text{XxXX}} = 3 \pm 2 \sqrt{2}$