Solve kE=1/2mv^2

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

Solve for E

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

Steps for Solving Linear Equation

The equation is in standard form.

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

Divide both sides by k.

$$\frac{kE}{k}=\frac{mv^{2}}{2k}$$

Dividing by k undoes the multiplication by k.

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

Solve for k

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

Steps for Solving Linear Equation

The equation is in standard form.

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

Divide both sides by E.

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

Dividing by E undoes the multiplication by E.

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