Solve 2x^2+xy-x^2=c

$$2 x ^ { 2 } + x y - x ^ { 2 } = c$$

Solve for c

$$c=x\left(x+y\right)$$

Solution Steps

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+xy=c$$

Swap sides so that all variable terms are on the left hand side.

$$c=x^{2}+xy$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y^{2}+4c}-y}{2}$$

$$x=\frac{-\sqrt{y^{2}+4c}-y}{2}$$

Solve for x

$$x=\frac{\sqrt{y^{2}+4c}-y}{2}$$

$$x=\frac{-\sqrt{y^{2}+4c}-y}{2}\text{, }c\geq -\frac{y^{2}}{4}$$