# How do you find the roots, real and imaginary, of y= x^2 -21x +(x+1)^2  using the quadratic formula?

Aug 10, 2017

$x = \frac{19 \pm \sqrt{353}}{4}$

#### Explanation:

We have: $y = {x}^{2} - 21 x + {\left(x + 1\right)}^{2}$

First, let's expand the parentheses:

$R i g h t a r r o w y = {x}^{2} - 21 x + {x}^{2} + 2 x + 1$

$R i g h t a r r o w y = 2 {x}^{2} - 19 x + 1$

Then, let's apply the quadratic formula:

$R i g h t a r r o w x = \frac{- \left(- 19\right) \pm \sqrt{{\left(- 19\right)}^{2} - 4 \left(2\right) \left(1\right)}}{2 \left(2\right)}$

$R i g h t a r r o w x = \frac{19 \pm \sqrt{361 - 8}}{4}$

$R i g h t a r r o w x = \frac{19 \pm \sqrt{353}}{4}$

Therefore, the solutions to the equation are $x = \frac{19 - \sqrt{353}}{4}$ and $x = \frac{19 + \sqrt{353}}{4}$.