# How do you solve w = sqrt[7w]  and find any extraneous solutions?

Apr 20, 2018

$w = 0 \mathmr{and} w = 7$

However we have a square root so for the solution in RRcolor(white)("d"); w>=0

#### Explanation:

Given: $w = \sqrt{7 w}$

Square both sides

${w}^{2} = 7 w$

Subtract $7 w$ from both sides

${w}^{2} - 7 w + 0 = 0$

compare to $a {w}^{2} + b w + c = 0 \textcolor{w h i t e}{\text{ddd") ->color(white)("ddd}} w = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$w = \frac{7 \pm \sqrt{{\left(- 7\right)}^{2} - 4 \left(1\right) \left(0\right)}}{2 \left(1\right)}$
$w = \frac{7}{2} \pm \frac{7}{2}$
$w = 0 \mathmr{and} w = 7$