Solve x^2-2yx+y=0

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

Solve for y

$$y=-\frac{x^{2}}{1-2x}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

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

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by -2x+1.

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

Dividing by -2x+1 undoes the multiplication by -2x+1.

$$y=-\frac{x^{2}}{1-2x}$$

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\sqrt{y\left(y-1\right)}+y\text{, }y\geq 1\text{ or }y\leq 0$$