Solve Ec=mv^2/2

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

Solve for E (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2Ec=mv^{2}$$

The equation is in standard form.

$$2cE=mv^{2}$$

Divide both sides by 2c.

$$\frac{2cE}{2c}=\frac{mv^{2}}{2c}$$

Dividing by 2c undoes the multiplication by 2c.

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

Solve for c (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2Ec=mv^{2}$$

Divide both sides by 2E.

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

Dividing by 2E undoes the multiplication by 2E.

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

Solve for E

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2Ec=mv^{2}$$

The equation is in standard form.

$$2cE=mv^{2}$$

Divide both sides by 2c.

$$\frac{2cE}{2c}=\frac{mv^{2}}{2c}$$

Dividing by 2c undoes the multiplication by 2c.

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

Solve for c

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2Ec=mv^{2}$$

Divide both sides by 2E.

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

Dividing by 2E undoes the multiplication by 2E.

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