Solve ax^2+c^2=0

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for a

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for c (complex solution)

$$c=-i\sqrt{a}x$$

$$c=i\sqrt{a}x$$

Solve for c

$$\left\{\begin{matrix}c=\sqrt{-a}x\text{; }c=-\sqrt{-a}x\text{, }&a\leq 0\\c=0\text{, }&x=0\end{matrix}\right.$$