Solve y=kx-x^2

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

Solve for k (complex solution)

$$\left\{\begin{matrix}k=x+\frac{y}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Add x^{2} to both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide y+x^{2} by x.

$$k=x+\frac{y}{x}$$

Solve for k

$$\left\{\begin{matrix}k=x+\frac{y}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Add x^{2} to both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide y+x^{2} by x.

$$k=x+\frac{y}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{k^{2}-4y}+k}{2}$$

$$x=\frac{-\sqrt{k^{2}-4y}+k}{2}$$

Solve for x

$$x=\frac{\sqrt{k^{2}-4y}+k}{2}$$

$$x=\frac{-\sqrt{k^{2}-4y}+k}{2}\text{, }y\leq \frac{k^{2}}{4}$$