How do you find the roots, real and imaginary, of y= x^2 + 8x -9- (-x-1)^2  using the quadratic formula?

Jan 10, 2016

x=5/3

Explanation:

There are no imaginary roots of this equation.
To get the roots, put y=0
Now expand ${\left(- x - 1\right)}^{2}$ which is actually ${\left(x + 1\right)}^{2}$

${x}^{2} + 8 x - 9 - \left({x}^{2} + 2 x + 1\right) = 0$

$\cancel{{x}^{2}} + 8 x - 9 \cancel{- {x}^{2}} - 2 x - 1 = 0$

$6 x - 10 = 0$

$x = \frac{5}{3}$

Additionally you can also see that this equation is actually equation of a straight line so it can have at most 1 zero (which is real).