Solve for k
\left\{\begin{matrix}k=-\frac{F}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&F=0\text{ and }x=0\end{matrix}\right.
Solve for F
F=-kx
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kx=m\frac{\mathrm{d}}{\mathrm{d}t}(x)-F
Subtract F from both sides.
xk=-F
The equation is in standard form.
\frac{xk}{x}=-\frac{F}{x}
Divide both sides by x.
k=-\frac{F}{x}
Dividing by x undoes the multiplication by x.
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