Solve 0=-x^2+kx+k

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

Solve for k

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

$$x\neq -1$$

Steps for Solving Linear Equation

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

$$-x^{2}+kx+k=0$$

Add x^{2} to both sides. Anything plus zero gives itself.

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

Combine all terms containing k.

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

Divide both sides by x+1.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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