# How do you solve sqrt [w+1]-5=2w and find any extraneous solutions?

Jul 5, 2016

$w = - \frac{19}{8} \pm \frac{\sqrt{23}}{8} i$

#### Explanation:

Add 5 to both sides, giving:

$\sqrt{w + 1} = 2 w + 5$

Square both sides

$w + 1 = {\left(2 w + 5\right)}^{2} = 4 {w}^{2} + 20 w + 25$

Collect like terms and solve the quadratic

$4 {w}^{2} + 19 w + 24 = 0$

$w = \frac{- 19 \pm \sqrt{{19}^{2} - 4 \left(4\right) \left(24\right)}}{2 \left(4\right)} = \frac{- 19 \pm \sqrt{- 23}}{8}$
$\sqrt{- 23} = \sqrt{23 {i}^{2}} = \sqrt{23} i$
$\implies w = - \frac{19}{8} \pm \frac{\sqrt{23}}{8} i$