Solve ax^2+bx+c^2=0

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract bx from both sides. Anything subtracted from zero gives its negation.

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

Subtract c^{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

Dividing by x^{2} undoes the multiplication by x^{2}.

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

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

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract c^{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

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

Solve for a

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

Steps for Solving Linear Equation

Subtract bx from both sides. Anything subtracted from zero gives its negation.

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

Subtract c^{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

Dividing by x^{2} undoes the multiplication by x^{2}.

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

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

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

Solve for b

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

Steps for Solving Linear Equation

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

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

Subtract c^{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

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