Solve E=1/2mv^2

$$E = \frac { 1 } { 2 } m v ^ { 2 }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{2E}{v^{2}}\text{, }&v\neq 0\\m\in \mathrm{C}\text{, }&E=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}mv^{2}=E$$

The equation is in standard form.

$$\frac{v^{2}}{2}m=E$$

Divide both sides by \frac{1}{2}v^{2}.

$$\frac{2\times \frac{v^{2}}{2}m}{v^{2}}=\frac{2E}{v^{2}}$$

Dividing by \frac{1}{2}v^{2} undoes the multiplication by \frac{1}{2}v^{2}.

$$m=\frac{2E}{v^{2}}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{2E}{v^{2}}\text{, }&v\neq 0\\m\in \mathrm{R}\text{, }&E=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}mv^{2}=E$$

The equation is in standard form.

$$\frac{v^{2}}{2}m=E$$

Divide both sides by \frac{1}{2}v^{2}.

$$\frac{2\times \frac{v^{2}}{2}m}{v^{2}}=\frac{2E}{v^{2}}$$

Dividing by \frac{1}{2}v^{2} undoes the multiplication by \frac{1}{2}v^{2}.

$$m=\frac{2E}{v^{2}}$$

Solve for E

$$E=\frac{mv^{2}}{2}$$