Solve Ap^2=s^2+12^2

$$A p ^ { 2 } = s ^ { 2 } + 12 ^ { 2 }$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{s^{2}+144}{p^{2}}\text{, }&p\neq 0\\A\in \mathrm{C}\text{, }&\left(s=-12i\text{ or }s=12i\right)\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$Ap^{2}=s^{2}+144$$

The equation is in standard form.

$$p^{2}A=s^{2}+144$$

Divide both sides by p^{2}.

$$\frac{p^{2}A}{p^{2}}=\frac{s^{2}+144}{p^{2}}$$

Dividing by p^{2} undoes the multiplication by p^{2}.

$$A=\frac{s^{2}+144}{p^{2}}$$

Solve for A

$$A=\frac{s^{2}+144}{p^{2}}$$

$$p\neq 0$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$Ap^{2}=s^{2}+144$$

The equation is in standard form.

$$p^{2}A=s^{2}+144$$

Divide both sides by p^{2}.

$$\frac{p^{2}A}{p^{2}}=\frac{s^{2}+144}{p^{2}}$$

Dividing by p^{2} undoes the multiplication by p^{2}.

$$A=\frac{s^{2}+144}{p^{2}}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-A^{-\frac{1}{2}}\sqrt{s^{2}+144}\text{; }p=A^{-\frac{1}{2}}\sqrt{s^{2}+144}\text{, }&A\neq 0\\p\in \mathrm{C}\text{, }&\left(s=-12i\text{ or }s=12i\right)\text{ and }A=0\end{matrix}\right.$$

Solve for p

$$p=\sqrt{\frac{s^{2}+144}{A}}$$

$$p=-\sqrt{\frac{s^{2}+144}{A}}\text{, }A>0$$