# The sum of the squares of two consecutive negative odd integers is equal to 514. How do you find the two integers?

Feb 21, 2016

-15 and -17

#### Explanation:

Two odd negative numbers: $n$ and $n + 2$.

The sum of squares=514:

${n}^{2} + {\left(n + 2\right)}^{2} = 514$

${n}^{2} + {n}^{2} + 4 n + 4 = 514$

$2 {n}^{2} + 4 n - 510 = 0$

$n = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \cdot 2 \cdot \left(- 510\right)}}{2 \cdot 2}$

$n = \frac{- 4 \pm \sqrt{16 + 4080}}{4}$

$n = \frac{- 4 \pm \sqrt{4096}}{4}$

$n = \frac{- 4 \pm 64}{4}$

$n = - \frac{68}{4} = - 17$ (because we want a negative number)

$n + 2 = - 15$