Solve T=2pisqrt{L/980}

$$T = 2 \pi \sqrt { \frac { L } { 980 } }$$

Solve for L

$$L=245\times \left(\frac{T}{\pi }\right)^{2}$$

$$T\geq 0$$

Steps for Solving Radical Equations

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

$$2\pi \sqrt{\frac{L}{980}}=T$$

Divide both sides by 2\pi .

$$\frac{2\pi \sqrt{\frac{1}{980}L}}{2\pi }=\frac{T}{2\pi }$$

Dividing by 2\pi undoes the multiplication by 2\pi .

$$\sqrt{\frac{1}{980}L}=\frac{T}{2\pi }$$

Square both sides of the equation.

$$\frac{1}{980}L=\frac{T^{2}}{4\pi ^{2}}$$

Multiply both sides by 980.

$$\frac{\frac{1}{980}L}{\frac{1}{980}}=\frac{T^{2}}{\frac{1}{980}\times 4\pi ^{2}}$$

Dividing by \frac{1}{980} undoes the multiplication by \frac{1}{980}.

$$L=\frac{T^{2}}{\frac{1}{980}\times 4\pi ^{2}}$$

Divide \frac{T^{2}}{4\pi ^{2}} by \frac{1}{980} by multiplying \frac{T^{2}}{4\pi ^{2}} by the reciprocal of \frac{1}{980}.

$$L=\frac{245T^{2}}{\pi ^{2}}$$

Solve for L (complex solution)

$$L=245\times \left(\frac{T}{\pi }\right)^{2}$$

$$|\frac{arg(T^{2})}{2}-arg(T)|<\pi \text{ or }T=0$$

Solve for T (complex solution)

$$T=\frac{\pi \sqrt{5L}}{35}$$

Solve for T

$$T=\frac{\pi \sqrt{5L}}{35}$$

$$L\geq 0$$