Solve F=k*frac{Q_{1}*Q_{2}}{r^2}[Q_{1}]

$$F = k \cdot \frac { Q _ { 1 } \cdot Q _ { 2 } } { r ^ { 2 } } [ Q _ { 1 } ]$$

Solve for Q_1 (complex solution)

$$\left\{\begin{matrix}Q_{1}=-Q_{2}^{-\frac{1}{2}}k^{-\frac{1}{2}}\sqrt{F}r\text{; }Q_{1}=Q_{2}^{-\frac{1}{2}}k^{-\frac{1}{2}}\sqrt{F}r\text{, }&Q_{2}\neq 0\text{ and }k\neq 0\text{ and }r\neq 0\\Q_{1}\in \mathrm{C}\text{, }&\left(Q_{2}=0\text{ or }k=0\right)\text{ and }F=0\text{ and }r\neq 0\end{matrix}\right.$$

Solve for F

$$F=\left(\frac{Q_{1}}{r}\right)^{2}Q_{2}k$$

$$r\neq 0$$

Solve for Q_1

$$\left\{\begin{matrix}Q_{1}=\sqrt{\frac{F}{Q_{2}k}}r\text{; }Q_{1}=-\sqrt{\frac{F}{Q_{2}k}}r\text{, }&\left(k>0\text{ or }Q_{2}<0\text{ or }F\leq 0\right)\text{ and }\left(F\geq 0\text{ or }Q_{2}<0\text{ or }k<0\right)\text{ and }k\neq 0\text{ and }Q_{2}\neq 0\text{ and }\left(k>0\text{ or }F\geq 0\text{ or }Q_{2}>0\right)\text{ and }r\neq 0\text{ and }\left(Q_{2}>0\text{ or }k<0\text{ or }F\leq 0\right)\\Q_{1}\in \mathrm{R}\text{, }&\left(Q_{2}=0\text{ or }k=0\right)\text{ and }F=0\text{ and }r\neq 0\end{matrix}\right.$$