# How do you solve using the completing the square method y^2 - 7y = -10?

May 18, 2017

$y = 5$
$y = 2$

#### Explanation:

${y}^{2} - 7 y = - 10$

${y}^{2} - 7 y + \frac{49}{4} = - 10 + \frac{49}{4} = \frac{- 40 + 49}{4} = \frac{9}{4}$
${\left(y - \frac{7}{2}\right)}^{2} = \frac{9}{4}$
$y - \frac{7}{2} = \pm \sqrt{\frac{9}{4}} = \frac{3}{2}$
$y = \frac{3}{2} + \frac{7}{2} = \frac{10}{2} = 5$
$y = - \frac{3}{2} + \frac{7}{2} = \frac{4}{2} = 2$

$y = 5$
$y = 2$