# How do you find the roots, real and imaginary, of y=-x^2-12x -7 using the quadratic formula?

$12 \pm \sqrt{29}$. There are no imaginary roots.

#### Explanation:

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

and $a = - 1 , b = - 12 , c = - 7$

Now let's substitute in:

$x = \frac{12 \pm \sqrt{{\left(- 12\right)}^{2} - 4 \left(- 1\right) \left(- 7\right)}}{2 \left(- 1\right)}$

and now simplify:

$x = 12 \pm \frac{\sqrt{\left(144 - 28\right)}}{-} 2$

$x = 12 \pm \frac{\sqrt{116}}{-} 2 = 12 \pm \frac{2 \sqrt{29}}{-} 2 = 12 \pm \sqrt{29}$

There are no imaginary roots. To explicitly state there are no imaginary roots, we can write the answer this way:

$x = 12 + \sqrt{29} + 0 i , 12 - \sqrt{29} + 0 i$