Solve x=40-10t^2A

$$x = 40 - 10 t ^ { 2 } A$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{40-x}{10t^{2}}\text{, }&t\neq 0\\A\in \mathrm{C}\text{, }&x=40\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$40-10t^{2}A=x$$

Subtract 40 from both sides.

$$-10t^{2}A=x-40$$

The equation is in standard form.

$$\left(-10t^{2}\right)A=x-40$$

Divide both sides by -10t^{2}.

$$\frac{\left(-10t^{2}\right)A}{-10t^{2}}=\frac{x-40}{-10t^{2}}$$

Dividing by -10t^{2} undoes the multiplication by -10t^{2}.

$$A=\frac{x-40}{-10t^{2}}$$

Divide x-40 by -10t^{2}.

$$A=-\frac{x-40}{10t^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{40-x}{10t^{2}}\text{, }&t\neq 0\\A\in \mathrm{R}\text{, }&x=40\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$40-10t^{2}A=x$$

Subtract 40 from both sides.

$$-10t^{2}A=x-40$$

The equation is in standard form.

$$\left(-10t^{2}\right)A=x-40$$

Divide both sides by -10t^{2}.

$$\frac{\left(-10t^{2}\right)A}{-10t^{2}}=\frac{x-40}{-10t^{2}}$$

Dividing by -10t^{2} undoes the multiplication by -10t^{2}.

$$A=\frac{x-40}{-10t^{2}}$$

Divide x-40 by -10t^{2}.

$$A=-\frac{x-40}{10t^{2}}$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=-\frac{iA^{-\frac{1}{2}}\sqrt{10\left(x-40\right)}}{10}\text{; }t=\frac{iA^{-\frac{1}{2}}\sqrt{10\left(x-40\right)}}{10}\text{, }&A\neq 0\\t\in \mathrm{C}\text{, }&x=40\text{ and }A=0\end{matrix}\right.$$

Solve for t

$$\left\{\begin{matrix}t=\frac{\sqrt{-\frac{10\left(x-40\right)}{A}}}{10}\text{; }t=-\frac{\sqrt{-\frac{10\left(x-40\right)}{A}}}{10}\text{, }&\left(A>0\text{ and }x\leq 40\right)\text{ or }\left(x\geq 40\text{ and }A<0\right)\\t\in \mathrm{R}\text{, }&x=40\text{ and }A=0\end{matrix}\right.$$