Solve θ^2x=θ^5

$$\theta ^ { 2 } x = \theta ^ { 5 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\theta ^{3}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&\theta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\theta ^{2}x=\theta ^{5}$$

Divide both sides by \theta ^{2}.

$$\frac{\theta ^{2}x}{\theta ^{2}}=\frac{\theta ^{5}}{\theta ^{2}}$$

Dividing by \theta ^{2} undoes the multiplication by \theta ^{2}.

$$x=\frac{\theta ^{5}}{\theta ^{2}}$$

Divide \theta ^{5} by \theta ^{2}.

$$x=\theta ^{3}$$

Solve for x

$$\left\{\begin{matrix}\\x=\theta ^{3}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\theta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\theta ^{2}x=\theta ^{5}$$

Divide both sides by \theta ^{2}.

$$\frac{\theta ^{2}x}{\theta ^{2}}=\frac{\theta ^{5}}{\theta ^{2}}$$

Dividing by \theta ^{2} undoes the multiplication by \theta ^{2}.

$$x=\frac{\theta ^{5}}{\theta ^{2}}$$

Divide \theta ^{5} by \theta ^{2}.

$$x=\theta ^{3}$$

Solve for θ (complex solution)

$$\theta =e^{\frac{2\pi i}{3}}\sqrt[3]{x}$$

$$\theta =\sqrt[3]{x}$$

$$\theta =e^{\frac{4\pi i}{3}}\sqrt[3]{x}$$

$$\theta =0$$

Solve for θ

$$\theta =0$$

$$\theta =\sqrt[3]{x}$$