Solve x^2-2x+2y=0

$${ x }^{ 2 } -2x+2y = 0$$

Solve for y

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add 2x to both sides.

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

The equation is in standard form.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide x\left(2-x\right) by 2.

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

Solve for x (complex solution)

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

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

Solve for x

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

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