# How do you find the roots, real and imaginary, of y=(2x-8)(x-2)-x^2-x  using the quadratic formula?

Dec 6, 2015

$x \cong 13.844 \mathmr{and} x \cong 1.156$

#### Explanation:

Step 1: Multiply/FOIL the expression

$y = \left(2 x - 8\right) \left(x - 2\right) - {x}^{2} - x$
$y = 2 {x}^{2} - 4 x - 8 x + 16 - {x}^{2} - x$
$y = {x}^{2} - 15 x + 16$

Step 2: Set the equation equal to zero
$0 = {x}^{2} - 15 x + 16$

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

$a = 1 , b = - 15 , c = 16$

Substitute into the formula

$x = \frac{- \left(- 15\right) \pm \sqrt{{\left(- 15\right)}^{2} - 4 \left(1\right) \left(16\right)}}{2}$

$x = \frac{15 \pm \sqrt{225 - 64}}{2}$

$x = \frac{15 + \sqrt{161}}{2}$

$x = \frac{15 \pm \left(12.688577\right)}{2}$

$x = \frac{15 + 12.688577}{2} = 13.844288$ or

$x = \frac{15 - 12.688577}{2} = 1.1557115$