How do you solve \sqrt { 2x + 48} = x?

Dec 16, 2016

$\left\{8\right\}$.

Explanation:

Square both sides:

${\left(\sqrt{2 x + 48}\right)}^{2} = {x}^{2}$

$2 x + 48 = {x}^{2}$

$0 = {x}^{2} - 2 x - 48$

$0 = \left(x - 8\right) \left(x + 6\right)$

$x = 8 \mathmr{and} - 6$

Check, as extraneous solutions may have been introduced in the solving process.

sqrt(2(8) + 48) =^? 8

sqrt(64) = 8" "color(green)(√)

AND

sqrt(2(-6) + 48) =^? -6

$\sqrt{36} \ne - 6 \text{ } \textcolor{red}{\times}$

Hopefully this helps!