Solve x^2+dz=0

$$x ^ { 2 } + d z = 0$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

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

$$dz=-x^{2}$$

The equation is in standard form.

$$zd=-x^{2}$$

Divide both sides by z.

$$\frac{zd}{z}=-\frac{x^{2}}{z}$$

Dividing by z undoes the multiplication by z.

$$d=-\frac{x^{2}}{z}$$

Solve for d

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

Steps for Solving Linear Equation

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

$$dz=-x^{2}$$

The equation is in standard form.

$$zd=-x^{2}$$

Divide both sides by z.

$$\frac{zd}{z}=-\frac{x^{2}}{z}$$

Dividing by z undoes the multiplication by z.

$$d=-\frac{x^{2}}{z}$$

Solve for x (complex solution)

$$x=-i\sqrt{d}\sqrt{z}$$

$$x=i\sqrt{d}\sqrt{z}$$

Solve for x

$$x=\sqrt{-dz}$$

$$x=-\sqrt{-dz}\text{, }\left(z\geq 0\text{ and }d\leq 0\right)\text{ or }\left(d\geq 0\text{ and }z\leq 0\right)$$