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

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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

Solve for b

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

Steps for Solving Linear Equation

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

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

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

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

Solve for a (complex solution)

$$a=-i\sqrt{bx^{2}+c}$$

$$a=i\sqrt{bx^{2}+c}$$

Solve for a

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

$$a=-\sqrt{-bx^{2}-c}\text{, }b\leq -\frac{c}{x^{2}}\text{ or }x=0$$