# How do you find the roots, real and imaginary, of y=-(2x-1)^2 -4x^2 - 13x + 4  using the quadratic formula?

Jun 29, 2016

$x = \frac{9 \pm \sqrt{177}}{-} 16$

#### Explanation:

Simplify the pattern step by step
$y = - {\left(2 x - 1\right)}^{2} - 4 {x}^{2} - 13 x + 4$
$y = - \left(4 {x}^{2} - 4 x + 1\right) - 4 {x}^{2} - 13 x + 4$
$y = - 8 {x}^{2} - 9 x + 3$
$x = \frac{9 \pm \sqrt{81 + 4 \cdot 8 \cdot 3}}{-} 16$
$x = \frac{9 \pm \sqrt{177}}{-} 16$