# How do you find the roots, real and imaginary, of y=-2(x+1)^2-(x-3)^2-10  using the quadratic formula?

Jun 9, 2018

color(blue)(x = (1 - isqrt62)/3, (1 + i sqrt62) / 3

#### Explanation:

$y = - 2 {\left(x + 1\right)}^{2} - {\left(x - 3\right)}^{2} - 10$

$y = - 2 {x}^{2} - 4 x - 2 - {x}^{2} + 6 x - 9 - 10$

$y = - 3 {x}^{2} + 2 x - 21$

$a = - 3 , b = 2 , c = = - 21$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{- 2 \pm \sqrt{4 - 252}}{-} 6$

color(blue)(x = (1 - isqrt62)/3, (1 + i sqrt62) / 3