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

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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

Solve for a

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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

Solve for b

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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