Solve x^2+2y+x=2

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

Solve for y

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

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

Subtract x from both sides.

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

The equation is in standard form.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{9-8y}-1}{2}$$

$$x=\frac{-\sqrt{9-8y}-1}{2}$$

Solve for x

$$x=\frac{\sqrt{9-8y}-1}{2}$$

$$x=\frac{-\sqrt{9-8y}-1}{2}\text{, }y\leq \frac{9}{8}$$