Solve sqrt{x}+sqrt{y}=10

$$\sqrt{ x } + \sqrt{ y } =10$$

Solve for x

$$x=\left(-\sqrt{y}+10\right)^{2}$$

$$y\geq 0\text{ and }-\sqrt{y}+10\geq 0$$

Steps for Solving Radical Equations

Subtract \sqrt{y} from both sides of the equation.

$$\sqrt{x}+\sqrt{y}-\sqrt{y}=10-\sqrt{y}$$

Subtracting \sqrt{y} from itself leaves 0.

$$\sqrt{x}=10-\sqrt{y}$$

Subtract \sqrt{y} from 10.

$$\sqrt{x}=-\sqrt{y}+10$$

Square both sides of the equation.

$$x=\left(-\sqrt{y}+10\right)^{2}$$

Solve for y

$$y=\left(-\sqrt{x}+10\right)^{2}$$

$$x\geq 0\text{ and }-\sqrt{x}+10\geq 0$$

Steps for Solving Radical Equations

Subtract \sqrt{x} from both sides of the equation.

$$\sqrt{y}+\sqrt{x}-\sqrt{x}=10-\sqrt{x}$$

Subtracting \sqrt{x} from itself leaves 0.

$$\sqrt{y}=10-\sqrt{x}$$

Subtract \sqrt{x} from 10.

$$\sqrt{y}=-\sqrt{x}+10$$

Square both sides of the equation.

$$y=\left(-\sqrt{x}+10\right)^{2}$$

Solve for x (complex solution)

$$x=\left(-\sqrt{y}+10\right)^{2}$$

$$y=100\text{ or }arg(-\sqrt{y}+10)<\pi$$

Solve for y (complex solution)

$$y=\left(-\sqrt{x}+10\right)^{2}$$

$$x=100\text{ or }arg(-\sqrt{x}+10)<\pi$$