Solve sqrt{x}=sqrt{y}-8

$$\sqrt { x } = \sqrt { y } - 8$$

Solve for x

$$x=\left(-\sqrt{y}+8\right)^{2}$$

$$y\geq 0\text{ and }-\left(-\sqrt{y}+8\right)\geq 0$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$x=\left(\sqrt{y}-8\right)^{2}$$

Solve for x (complex solution)

$$x=\left(-\sqrt{y}+8\right)^{2}$$

$$y=64\text{ or }arg(-\sqrt{y}+8)\geq \pi$$

Solve for y (complex solution)

$$y=\left(\sqrt{x}+8\right)^{2}$$

$$arg(\sqrt{x}+8)<\pi$$

Solve for y

$$y=\left(\sqrt{x}+8\right)^{2}$$

$$x\geq 0$$