Solve y=x^2+ax+1

$$y = x ^ { 2 } + a x + 1$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{-x^{2}+y-1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+ax+1=y$$

Subtract x^{2} from both sides.

$$ax+1=y-x^{2}$$

Subtract 1 from both sides.

$$ax=y-x^{2}-1$$

The equation is in standard form.

$$xa=-x^{2}+y-1$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Solve for a

$$\left\{\begin{matrix}a=\frac{-x^{2}+y-1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+ax+1=y$$

Subtract x^{2} from both sides.

$$ax+1=y-x^{2}$$

Subtract 1 from both sides.

$$ax=y-x^{2}-1$$

The equation is in standard form.

$$xa=-x^{2}+y-1$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=\frac{-\sqrt{4y+a^{2}-4}-a}{2}\text{, }y\geq -\frac{a^{2}}{4}+1$$