Solve x+y^2=14x+y

$$x + y ^ { 2 } = 14 x + y$$

Solve for x

$$x=\frac{y\left(y-1\right)}{13}$$

Steps for Solving Linear Equation

Subtract 14x from both sides.

$$x+y^{2}-14x=y$$

Combine x and -14x to get -13x.

$$-13x+y^{2}=y$$

Subtract y^{2} from both sides.

$$-13x=y-y^{2}$$

Divide both sides by -13.

$$\frac{-13x}{-13}=\frac{y\left(1-y\right)}{-13}$$

Dividing by -13 undoes the multiplication by -13.

$$x=\frac{y\left(1-y\right)}{-13}$$

Divide y\left(1-y\right) by -13.

$$x=-\frac{y\left(1-y\right)}{13}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{52x+1}+1}{2}$$

$$y=\frac{-\sqrt{52x+1}+1}{2}$$

Solve for y

$$y=\frac{\sqrt{52x+1}+1}{2}$$

$$y=\frac{-\sqrt{52x+1}+1}{2}\text{, }x\geq -\frac{1}{52}$$