Solve y=x^2+ax+a

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x^{2}-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&y=1\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+ax+a=y$$

Subtract x^{2} from both sides.

$$ax+a=y-x^{2}$$

Combine all terms containing a.

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

Divide both sides by x+1.

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

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

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{x^{2}-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&y=1\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+ax+a=y$$

Subtract x^{2} from both sides.

$$ax+a=y-x^{2}$$

Combine all terms containing a.

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

Divide both sides by x+1.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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