How do you solve 3(x-5)^2 + 8 = 14?

Jul 7, 2016

$x = 5 \pm \sqrt{2.}$

$x \cong 6.414$, or, $x \cong 3.586$

Explanation:

$3 {\left(x - 5\right)}^{2} + 8 = 14.$
$\therefore 3 {\left(x - 5\right)}^{2} = 14 - 8 = 6.$
$\therefore {\left(x - 5\right)}^{2} = \frac{6}{3} = 2.$
$\therefore \left(x - 5\right) = \pm \sqrt{2.}$
$\therefore x = 5 \pm \sqrt{2.}$

Taking, $\sqrt{2} = 1.414 , x \cong 5 \pm 1.414 .$

$\therefore x \cong 5 + 1.414 = 6.414$, or, $x \cong 5 - 1.414 = 3.586$