Solve a^2+bx+c=0

$$a ^ { 2 } + b x + c = 0$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract a^{2} from both sides. Anything subtracted from zero gives its negation.

$$bx+c=-a^{2}$$

Subtract c from both sides.

$$bx=-a^{2}-c$$

The equation is in standard form.

$$xb=-a^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-a^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-a^{2}-c}{x}$$

Divide -a^{2}-c by x.

$$b=-\frac{a^{2}+c}{x}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract a^{2} from both sides. Anything subtracted from zero gives its negation.

$$bx+c=-a^{2}$$

Subtract c from both sides.

$$bx=-a^{2}-c$$

The equation is in standard form.

$$xb=-a^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-a^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-a^{2}-c}{x}$$

Divide -a^{2}-c by x.

$$b=-\frac{a^{2}+c}{x}$$

Solve for a (complex solution)

$$a=-i\sqrt{bx+c}$$

$$a=i\sqrt{bx+c}$$

Solve for a

$$a=\sqrt{-bx-c}$$

$$a=-\sqrt{-bx-c}\text{, }c\leq -bx$$