Solve BC^2=AB^2+AC^2

$$B C ^ { 2 } = A B ^ { 2 } + A C ^ { 2 }$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{BC^{2}}{B^{2}+C^{2}}\text{, }&B\neq iC\text{ and }B\neq -iC\\A\in \mathrm{C}\text{, }&C=0\text{ and }B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$AB^{2}+AC^{2}=BC^{2}$$

Combine all terms containing A.

$$\left(B^{2}+C^{2}\right)A=BC^{2}$$

Divide both sides by B^{2}+C^{2}.

$$\frac{\left(B^{2}+C^{2}\right)A}{B^{2}+C^{2}}=\frac{BC^{2}}{B^{2}+C^{2}}$$

Dividing by B^{2}+C^{2} undoes the multiplication by B^{2}+C^{2}.

$$A=\frac{BC^{2}}{B^{2}+C^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{BC^{2}}{B^{2}+C^{2}}\text{, }&C\neq 0\text{ or }B\neq 0\\A\in \mathrm{R}\text{, }&B=0\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$AB^{2}+AC^{2}=BC^{2}$$

Combine all terms containing A.

$$\left(B^{2}+C^{2}\right)A=BC^{2}$$

Divide both sides by B^{2}+C^{2}.

$$\frac{\left(B^{2}+C^{2}\right)A}{B^{2}+C^{2}}=\frac{BC^{2}}{B^{2}+C^{2}}$$

Dividing by B^{2}+C^{2} undoes the multiplication by B^{2}+C^{2}.

$$A=\frac{BC^{2}}{B^{2}+C^{2}}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\frac{\sqrt{C^{2}\left(C^{2}-4A^{2}\right)}-C^{2}}{2A}\text{; }B=\frac{\sqrt{C^{2}\left(C^{2}-4A^{2}\right)}+C^{2}}{2A}\text{, }&A\neq 0\\B=0\text{, }&A=0\text{ and }C\neq 0\\B\in \mathrm{C}\text{, }&A=0\text{ and }C=0\end{matrix}\right.$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{C\left(\sqrt{C^{2}-4A^{2}}-C\right)}{2A}\text{; }B=\frac{C\left(\sqrt{C^{2}-4A^{2}}+C\right)}{2A}\text{, }&A\neq 0\text{ and }|C|\geq 2|A|\\B=0\text{, }&C=0\text{ or }A=0\\B\in \mathrm{R}\text{, }&A=0\text{ and }C=0\end{matrix}\right.$$