Solve {l}{1/2mv^2=mgL+mgL/2}{g=10quadv=}

$$\left. \begin{array} { l } { \frac { 1 } { 2 } m v ^ { 2 } = m g L + m g \frac { L } { 2 } } \\ { g = 10 \quad v = } \end{array} \right.$$

Solve for m, v, g, L (complex solution)

$$\left\{\begin{matrix}\\m=0\text{, }v=\frac{g}{10}\text{, }g\neq 0\text{, }L\in \mathrm{C}\text{; }m\in \mathrm{C}\text{, }v=0\text{, }g=0\text{, }L\in \mathrm{C}\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }v=\frac{g}{10}\text{, }g\neq 0\text{, }L=\frac{g}{300}\text{, }&g\neq 0\end{matrix}\right.$$

Solve for m, v, g, L

$$\left\{\begin{matrix}\\m=0\text{, }v=\frac{g}{10}\text{, }g\neq 0\text{, }L\in \mathrm{R}\text{; }m\in \mathrm{R}\text{, }v=0\text{, }g=0\text{, }L\in \mathrm{R}\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }v=-\frac{|g|}{10}\text{, }g<0\text{, }L=\frac{g}{300}\text{; }m\in \mathrm{R}\text{, }v=\frac{|g|}{10}\text{, }g>0\text{, }L=\frac{g}{300}\text{, }&g\neq 0\end{matrix}\right.$$