Solve p^2=x/a

$$p ^ { 2 } = \frac { x } { a }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x}{p^{2}}\text{, }&x\neq 0\text{ and }p\neq 0\\a\neq 0\text{, }&p=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$ap^{2}=x$$

The equation is in standard form.

$$p^{2}a=x$$

Divide both sides by p^{2}.

$$\frac{p^{2}a}{p^{2}}=\frac{x}{p^{2}}$$

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

$$a=\frac{x}{p^{2}}$$

Variable a cannot be equal to 0.

$$a=\frac{x}{p^{2}}\text{, }a\neq 0$$

Solve for p (complex solution)

$$p=-a^{-\frac{1}{2}}\sqrt{x}$$

$$p=a^{-\frac{1}{2}}\sqrt{x}\text{, }a\neq 0$$

Solve for p

$$p=\sqrt{\frac{x}{a}}$$

$$p=-\sqrt{\frac{x}{a}}\text{, }\left(x\geq 0\text{ and }a>0\right)\text{ or }\left(x\leq 0\text{ and }a<0\right)$$