# How do you find the roots, real and imaginary, of y= -2x^2 - 5x + 6 - (x-5)^2  using the quadratic formula?

Aug 18, 2017

You gotta write it in standard form...

#### Explanation:

first, multiply out:

$y = - 2 {x}^{2} - 5 x + 6 - \left({x}^{2} - 10 x + 25\right)$
$= - 2 {x}^{2} - 5 x + 6 - {x}^{2} + 10 x - 25$

...now, collect the terms

$= - 3 {x}^{2} + 5 x - 19$

...and now you have your coefficients a, b, and c:

a = -3, b = 5, c = -19

...that you can plug into the quadratic formula:

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

...and I'll bet you can take it from here.

GOOD LUCK