# How do you solve w- 1= \sqrt { - 19+ 7w }?

Mar 19, 2018

The solutions are $w = 4 , 5$.

#### Explanation:

Square both sides of the equation, combine like terms, then factor the new quadratic. Here's what that process looks like:

$w - 1 = \sqrt{- 19 + 7 w}$

${\left(w - 1\right)}^{2} = {\left(\sqrt{- 19 + 7 w}\right)}^{2}$

${\left(w - 1\right)}^{2} = - 19 + 7 w$

$\left(w - 1\right) \left(w - 1\right) = - 19 + 7 w$

${w}^{2} - w - w + 1 = - 19 + 7 w$

${w}^{2} - 2 w + 1 = - 19 + 7 w$

${w}^{2} - 9 w + 1 = - 19$

${w}^{2} - 9 w + 20 = 0$

$\left(w - 4\right) \left(w - 5\right) = 0$

$w = 4 , 5$

Those are the solutions. Hope this helped!