Solve wrt x = ∫ (v_{0}+ct)dt

$$d x = \int ( v _ { 0 } + c t ) d t$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{ct^{2}+2tv_{0}+С}{2x}\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&С=\frac{ct^{2}}{2}+tv_{0}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xd=\frac{ct^{2}}{2}+tv_{0}+С$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{\frac{ct^{2}}{2}+tv_{0}+С}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{\frac{ct^{2}}{2}+tv_{0}+С}{x}$$

Divide v_{0}t+\frac{ct^{2}}{2}+С by x.

$$d=\frac{ct^{2}+2tv_{0}+2С}{2x}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{ct^{2}+2tv_{0}+С}{2x}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&С=\frac{ct^{2}}{2}+tv_{0}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xd=\frac{ct^{2}}{2}+tv_{0}+С$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{\frac{ct^{2}}{2}+tv_{0}+С}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{\frac{ct^{2}}{2}+tv_{0}+С}{x}$$

Divide v_{0}t+\frac{ct^{2}}{2}+С by x.

$$d=\frac{ct^{2}+2tv_{0}+2С}{2x}$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{dx-tv_{0}-С}{t^{2}}\text{, }&t\neq 0\\c\in \mathrm{C}\text{, }&С=dx\text{ and }t=0\end{matrix}\right.$$

Solve for c

$$\left\{\begin{matrix}c=\frac{dx-tv_{0}-С}{t^{2}}\text{, }&t\neq 0\\c\in \mathrm{R}\text{, }&С=dx\text{ and }t=0\end{matrix}\right.$$