Solve Ta^2t=1

$$T a ^ { 2 } t = 1$$

Solve for T

$$T=\frac{1}{ta^{2}}$$

$$t\neq 0\text{ and }a\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$ta^{2}T=1$$

Divide both sides by a^{2}t.

$$\frac{ta^{2}T}{ta^{2}}=\frac{1}{ta^{2}}$$

Dividing by a^{2}t undoes the multiplication by a^{2}t.

$$T=\frac{1}{ta^{2}}$$

Solve for a (complex solution)

$$a=-T^{-\frac{1}{2}}t^{-\frac{1}{2}}$$

$$a=T^{-\frac{1}{2}}t^{-\frac{1}{2}}\text{, }t\neq 0\text{ and }T\neq 0$$

Solve for a

$$a=\frac{1}{\sqrt{Tt}}$$

$$a=-\frac{1}{\sqrt{Tt}}\text{, }\left(t>0\text{ and }T>0\right)\text{ or }\left(T<0\text{ and }t<0\right)$$