# How do you solve sqrt(x+7) = x + 1 and find any extraneous solutions?

Apr 19, 2018

I tried this:

#### Explanation:

Let us square both sides:

${\left(\sqrt{x + 7}\right)}^{2} = {\left(x + 1\right)}^{2}$

$x + 7 = {x}^{2} + 2 x + 1$

rearrange:

${x}^{2} + x - 6 = 0$

${x}_{1 , 2} = \frac{- 1 \pm \sqrt{1 + 24}}{2} = \frac{- 1 \pm 5}{2}$

giving:

${x}_{1} = - 3$ that doesn't work;
${x}_{2} = 2$.