Solve s=xt+at^2/2

$$s = x t + \frac { a t ^ { 2 } } { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{2\left(tx-s\right)}{t^{2}}\text{, }&t\neq 0\\a\in \mathrm{C}\text{, }&s=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xt+\frac{at^{2}}{2}=s$$

Subtract xt from both sides.

$$\frac{at^{2}}{2}=s-xt$$

Multiply both sides of the equation by 2.

$$at^{2}=2s-2xt$$

The equation is in standard form.

$$t^{2}a=2s-2tx$$

Divide both sides by t^{2}.

$$\frac{t^{2}a}{t^{2}}=\frac{2s-2tx}{t^{2}}$$

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

$$a=\frac{2s-2tx}{t^{2}}$$

Divide 2s-2xt by t^{2}.

$$a=\frac{2\left(s-tx\right)}{t^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2\left(tx-s\right)}{t^{2}}\text{, }&t\neq 0\\a\in \mathrm{R}\text{, }&s=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xt+\frac{at^{2}}{2}=s$$

Subtract xt from both sides.

$$\frac{at^{2}}{2}=s-xt$$

Multiply both sides of the equation by 2.

$$at^{2}=2s-2xt$$

The equation is in standard form.

$$t^{2}a=2s-2tx$$

Divide both sides by t^{2}.

$$\frac{t^{2}a}{t^{2}}=\frac{2s-2tx}{t^{2}}$$

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

$$a=\frac{2s-2tx}{t^{2}}$$

Divide 2s-2xt by t^{2}.

$$a=\frac{2\left(s-tx\right)}{t^{2}}$$

Solve for s

$$s=\frac{t\left(2x+at\right)}{2}$$