# How do you find the roots, real and imaginary, of y= 2x^2 - 2x - (x-9)^2  using the quadratic formula?

Jul 14, 2018

$x = - 8 \pm \sqrt{145}$

#### Explanation:

Simplifying the given equation and using the Formula
${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$

we get
$2 {x}^{2} - 2 x - \left({x}^{2} - 18 x + 81\right) = 0$ combinging like Terms

${x}^{2} + 16 x - 81 = 0$

${x}^{2} + p x + q = 0$
${x}_{1 , 2} = - \frac{p}{2} \pm \sqrt{{\left(\frac{p}{2}\right)}^{2} - q}$
${x}_{1 , 2} = - 8 \pm \sqrt{64 + 81}$
${x}_{1 , 2} = - 8 \pm \sqrt{145}$