Solve x^2=y(1+x)

$$x ^ { 2 } = y ( 1 + x )$$

Solve for y

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

$$x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by 1+x.

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

Swap sides so that all variable terms are on the left hand side.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1+x.

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{y\left(y+4\right)}+y}{2}$$

$$x=\frac{-\sqrt{y\left(y+4\right)}+y}{2}$$

Solve for x

$$x=\frac{\sqrt{y\left(y+4\right)}+y}{2}$$

$$x=\frac{-\sqrt{y\left(y+4\right)}+y}{2}\text{, }y\leq -4\text{ or }y\geq 0$$