# How do you solve sqrt (x+2) +4 = x and find any extraneous solutions?

May 6, 2018

color(maroon)("Solutions : " x = 2, 7

#### Explanation:

$\sqrt{x + 2} + 4 = x$

$\sqrt{x + 2} = x - 4$

Squaring both sides, $x + 2 = {\left(x - 4\right)}^{2}$

$x + 2 = {x}^{2} - 8 x + 16$

${x}^{2} - 9 x + 14 = 0$

${x}^{2} - 2 x - 7 x + 14 = 0$

$x \left(x - 2\right) - 7 \left(x - 2\right) = 0$

$\left(x - 2\right) \cdot \left(x - 7\right) = 0$

$x = 2 , 7$