Solve x^2+y=x-y

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

Solve for y

$$y=-\frac{x\left(x-1\right)}{2}$$

Steps for Solving Linear Equation

Add y to both sides.

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

Combine y and y to get 2y.

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

Subtract x^{2} from both sides.

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

Divide both sides by 2.

$$\frac{2y}{2}=\frac{x\left(1-x\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{x\left(1-x\right)}{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{1-8y}+1}{2}$$

$$x=\frac{-\sqrt{1-8y}+1}{2}$$

Solve for x

$$x=\frac{\sqrt{1-8y}+1}{2}$$

$$x=\frac{-\sqrt{1-8y}+1}{2}\text{, }y\leq \frac{1}{8}$$