Solve F^2=ab

$$F ^ { 2 } = a b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{F^{2}}{b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&F=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ab=F^{2}$$

The equation is in standard form.

$$ba=F^{2}$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{F^{2}}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{F^{2}}{b}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{F^{2}}{b}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&F=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ab=F^{2}$$

The equation is in standard form.

$$ba=F^{2}$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{F^{2}}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{F^{2}}{b}$$

Solve for F (complex solution)

$$F=-\sqrt{a}\sqrt{b}$$

$$F=\sqrt{a}\sqrt{b}$$

Solve for F

$$F=\sqrt{ab}$$

$$F=-\sqrt{ab}\text{, }\left(b\geq 0\text{ and }a\geq 0\right)\text{ or }\left(a\leq 0\text{ and }b\leq 0\right)$$