# How do you find the roots, real and imaginary, of y= x^2 - 8x + (x+4)^2  using the quadratic formula?

May 12, 2018

color(maroon)("two roots are " +2sqrt2 i, -2sqrt2 i

#### Explanation:

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

$y = {x}^{2} - 8 x + {x}^{2} + 8 x + 16$

$y = 2 {x}^{2} + 16$

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

$a = 2 , b = 0 , c = 16$

$x = \frac{0 \pm \sqrt{0 - 128}}{4}$

$x = \pm 8 \frac{\sqrt{- 2}}{4} = \pm 2 \sqrt{- 2}$

color(maroon)(x = + 2sqrt2 i, -2sqrt2 i