Solve alpha=p+sqrt{y}

$$\alpha = p + \sqrt { y }$$

Solve for y

$$y=\left(\alpha -p\right)^{2}$$

$$\alpha -p\geq 0$$

Steps for Solving Radical Equations

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

$$p+\sqrt{y}=\alpha$$

Subtract p from both sides.

$$\sqrt{y}=\alpha -p$$

Square both sides of the equation.

$$y=\left(\alpha -p\right)^{2}$$

Solve for p (complex solution)

$$p=\alpha -\sqrt{y}$$

Solve for y (complex solution)

$$y=\left(\alpha -p\right)^{2}$$

$$\alpha =p\text{ or }arg(\alpha -p)<\pi$$

Solve for p

$$p=\alpha -\sqrt{y}$$

$$y\geq 0$$