# How do you solve sqrt(x+6)-5=x+1 and find any extraneous solutions?

Aug 11, 2016

The Son. Set $= \left\{- 6 , - 5\right\}$.

There are no Extraneous Solns.

#### Explanation:

We rewrite the given eqn. as, $\sqrt{x + 6} = 5 + x + 1 = x + 6$

$\therefore {\left(\sqrt{x + 6}\right)}^{2} = {\left(x + 6\right)}^{2}$

$\therefore \left(x + 6\right) - {\left(x + 6\right)}^{2} = 0$

$\therefore \left(x + 6\right) \left(1 - x - 6\right) = 0$.

$\therefore - \left(x + 6\right) \left(x + 5\right) = 0$

$\therefore x = - 6 , \mathmr{and} , x = - 5$

these roots satisfy the given eqn.

Hence, The Son. Set $= \left\{- 6 , - 5\right\}$.

There are no Extraneous Solns.