Solve T-2pi=sqrt{L/g}

$$T - 2 \pi = \sqrt { \frac { L } { g } }$$

Solve for L

$$L=g\left(T-2\pi \right)^{2}$$

$$T-2\pi \geq 0\text{ and }g\neq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{\frac{L}{g}}=T-2\pi$$

Square both sides of the equation.

$$\frac{1}{g}L=\left(T-2\pi \right)^{2}$$

Divide both sides by g^{-1}.

$$\frac{\frac{1}{g}Lg}{1}=\frac{\left(T-2\pi \right)^{2}g}{1}$$

Dividing by g^{-1} undoes the multiplication by g^{-1}.

$$L=\frac{\left(T-2\pi \right)^{2}g}{1}$$

Divide \left(T-2\pi \right)^{2} by g^{-1}.

$$L=g\left(T-2\pi \right)^{2}$$

Solve for L (complex solution)

$$L=g\left(T-2\pi \right)^{2}$$

$$g\neq 0\text{ and }\left(T=2\pi \text{ or }arg(T-2\pi )<\pi \right)$$

Solve for T (complex solution)

$$T=\sqrt{\frac{L}{g}}+2\pi$$

$$g\neq 0$$

Solve for T

$$T=\sqrt{\frac{L}{g}}+2\pi$$

$$\left(L\geq 0\text{ and }g>0\right)\text{ or }\left(L\leq 0\text{ and }g<0\right)$$