# How do you solve a two variable 2nd degree polynomial

Somebody else already asked something similar although I believe this method does not apply to my case. Solving system of multivariable 2nd-degree polynomials

My problem is the following. I have:

x^2 + y^2 + 2xy - y

I need to solve for y. I am not good at math so this might be a silly question. I know how to solve single variable second degree polynomials, but cannot find the way to get the solution in the answer key:

y = -x - x^2 and y = -x + x^2

How can I do this? Is there a name for this formula or method? Thank you

• Apply quadratic formula to $(1)y^2 + (2x-1)y + x^2=0$, where I've grouped it to more clearly be a quadratic polynomial in $y$ (whose coefficients just happen to include some $x$s). – Eric Towers Feb 10 '14 at 10:42
• Thank you. Its clear now what to do. – user127623 Feb 10 '14 at 10:54

You should use the quadratic formula to the equation with respect to $y$: $$y^2 + (2x - 1) y + x^2 = 0.$$ This yields $$y = \frac{1 - 2x \pm \sqrt{ 1 - 4x } }{2}.$$ As this does not yield the answers you expect, perhaps you entered a wrong term in the problem expression?