Solve A=LxL

$$A = L x L$$

Solve for A

$$A=xL^{2}$$

Solution Steps

Multiply L and L to get L^{2}.

$$A=L^{2}x$$

Solve for L (complex solution)

$$\left\{\begin{matrix}L=-x^{-\frac{1}{2}}\sqrt{A}\text{; }L=x^{-\frac{1}{2}}\sqrt{A}\text{, }&x\neq 0\\L\in \mathrm{C}\text{, }&A=0\text{ and }x=0\end{matrix}\right.$$

Solve for L

$$\left\{\begin{matrix}L=\sqrt{\frac{A}{x}}\text{; }L=-\sqrt{\frac{A}{x}}\text{, }&\left(A\geq 0\text{ and }x>0\right)\text{ or }\left(A\leq 0\text{ and }x<0\right)\\L\in \mathrm{R}\text{, }&A=0\text{ and }x=0\end{matrix}\right.$$