Solve y=sqrt{2px}

$$y = \sqrt { 2 p x }$$

Solve for p

$$\left\{\begin{matrix}p=\frac{y^{2}}{2x}\text{, }&y\geq 0\text{ and }x\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{2px}=y$$

Square both sides of the equation.

$$2xp=y^{2}$$

Divide both sides by 2x.

$$\frac{2xp}{2x}=\frac{y^{2}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

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

Solve for x

$$\left\{\begin{matrix}x=\frac{y^{2}}{2p}\text{, }&y\geq 0\text{ and }p\neq 0\\x\in \mathrm{R}\text{, }&p=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{2px}=y$$

Square both sides of the equation.

$$2px=y^{2}$$

Divide both sides by 2p.

$$\frac{2px}{2p}=\frac{y^{2}}{2p}$$

Dividing by 2p undoes the multiplication by 2p.

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

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{y^{2}}{2x}\text{, }&x\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\p\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y^{2}}{2p}\text{, }&p\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\x\in \mathrm{C}\text{, }&y=0\text{ and }p=0\end{matrix}\right.$$