# How do you solve  ( x - 4)^2 = 12?

Mar 31, 2016

$x = 7.464$
$x = 0.536$

#### Explanation:

Given -

${\left(x - 4\right)}^{2} = 12$
${x}^{2} - 8 x + 16 = 12$
${x}^{2} - 8 x + 16 - 12 = 0$
${x}^{2} - 8 x + 4 = 0$
$x = \frac{- b \pm \sqrt{{b}^{2} - \left(4 a c\right)}}{2 a}$
$x = \frac{8 \pm \sqrt{{\left(- 8\right)}^{2} - \left(4 \times 1 \times 4\right)}}{2 \times 1}$
$x = \frac{8 \pm \sqrt{64 - 16}}{2}$
$x = \frac{8 \pm \sqrt{48}}{2}$
$x = \frac{8 \pm 6.928}{2}$
$x = \frac{8 + 6.928}{2} = \frac{14.928}{2} = 7.464$
$x = 7.464$
$x = \frac{8 - 6.928}{2} = \frac{1.072}{2} = 0.536$
$x = 0.536$