Solve f=msqrt{n^2+4}

$$f = m \sqrt { n ^ { 2 } + 4 }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\left(n^{2}+4\right)^{-\frac{1}{2}}f\text{, }&n\neq -2i\text{ and }n\neq 2i\\m\in \mathrm{C}\text{, }&\left(n=2i\text{ or }n=-2i\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$m\sqrt{n^{2}+4}=f$$

The equation is in standard form.

$$\sqrt{n^{2}+4}m=f$$

Divide both sides by \sqrt{n^{2}+4}.

$$\frac{\sqrt{n^{2}+4}m}{\sqrt{n^{2}+4}}=\frac{f}{\sqrt{n^{2}+4}}$$

Dividing by \sqrt{n^{2}+4} undoes the multiplication by \sqrt{n^{2}+4}.

$$m=\frac{f}{\sqrt{n^{2}+4}}$$

Divide f by \sqrt{n^{2}+4}.

$$m=\left(n^{2}+4\right)^{-\frac{1}{2}}f$$

Solve for m

$$m=\frac{f}{\sqrt{n^{2}+4}}$$

Steps for Solving Linear Equation

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

$$m\sqrt{n^{2}+4}=f$$

The equation is in standard form.

$$\sqrt{n^{2}+4}m=f$$

Divide both sides by \sqrt{n^{2}+4}.

$$\frac{\sqrt{n^{2}+4}m}{\sqrt{n^{2}+4}}=\frac{f}{\sqrt{n^{2}+4}}$$

Dividing by \sqrt{n^{2}+4} undoes the multiplication by \sqrt{n^{2}+4}.

$$m=\frac{f}{\sqrt{n^{2}+4}}$$

Solve for f

$$f=m\sqrt{n^{2}+4}$$