Solve x^2=-4ay

$$x ^ { 2 } = - 4 a y$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x^{2}}{4y}\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-4ay=x^{2}$$

The equation is in standard form.

$$\left(-4y\right)a=x^{2}$$

Divide both sides by -4y.

$$\frac{\left(-4y\right)a}{-4y}=\frac{x^{2}}{-4y}$$

Dividing by -4y undoes the multiplication by -4y.

$$a=\frac{x^{2}}{-4y}$$

Divide x^{2} by -4y.

$$a=-\frac{x^{2}}{4y}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{x^{2}}{4y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-4ay=x^{2}$$

The equation is in standard form.

$$\left(-4y\right)a=x^{2}$$

Divide both sides by -4y.

$$\frac{\left(-4y\right)a}{-4y}=\frac{x^{2}}{-4y}$$

Dividing by -4y undoes the multiplication by -4y.

$$a=\frac{x^{2}}{-4y}$$

Divide x^{2} by -4y.

$$a=-\frac{x^{2}}{4y}$$

Solve for x (complex solution)

$$x=-2i\sqrt{a}\sqrt{y}$$

$$x=2i\sqrt{a}\sqrt{y}$$

Solve for x

$$x=2\sqrt{-ay}$$

$$x=-2\sqrt{-ay}\text{, }\left(y\geq 0\text{ and }a\leq 0\right)\text{ or }\left(a\geq 0\text{ and }y\leq 0\right)$$