# How do you solve 5n^2 + 19n - 68 = -2 by completing the square?

May 24, 2015

$y = 5 \left({n}^{2} + 19 \frac{n}{5} - \frac{66}{5}\right)$

$\left({n}^{2} + 19 \frac{n}{5} + {\left(\frac{19}{10}\right)}^{2} - {\left(\frac{19}{10}\right)}^{2} - \frac{66}{5}\right)$ = 0

(n + 19/10)^2 = (361 + 132)/10)

${\left(n + \frac{19}{10}\right)}^{2} = \frac{493}{10} = 4.93$

$n + 1.9 = 2.22 - - n = 2.22 - 1.9 = 0.32$

$n + 1.9 = - 2.22 \to n = - 2.22 - 1.9 = - 4.12$