Solve sqrt{x-1}+sqrt{y+1}=8

$$\sqrt { x - 1 } + \sqrt { y + 1 } = 8$$

Solve for x

$$x=y-16\sqrt{y+1}+66$$

$$y\geq -1\text{ and }-\sqrt{y+1}+8\geq 0$$

Steps for Solving Radical Equations

Subtract \sqrt{y+1} from both sides of the equation.

$$\sqrt{x-1}+\sqrt{y+1}-\sqrt{y+1}=8-\sqrt{y+1}$$

Subtracting \sqrt{y+1} from itself leaves 0.

$$\sqrt{x-1}=8-\sqrt{y+1}$$

Subtract \sqrt{y+1} from 8.

$$\sqrt{x-1}=-\sqrt{y+1}+8$$

Square both sides of the equation.

$$x-1=\left(-\sqrt{y+1}+8\right)^{2}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\left(-\sqrt{y+1}+8\right)^{2}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\left(-\sqrt{y+1}+8\right)^{2}-\left(-1\right)$$

Subtract -1 from \left(8-\sqrt{y+1}\right)^{2}.

$$x=y-16\sqrt{y+1}+66$$

Solve for y

$$y=x-16\sqrt{x-1}+62$$

$$-\sqrt{x-1}+8\geq 0\text{ and }x\geq 1$$

Steps for Solving Radical Equations

Subtract \sqrt{x-1} from both sides of the equation.

$$\sqrt{y+1}+\sqrt{x-1}-\sqrt{x-1}=8-\sqrt{x-1}$$

Subtracting \sqrt{x-1} from itself leaves 0.

$$\sqrt{y+1}=8-\sqrt{x-1}$$

Subtract \sqrt{x-1} from 8.

$$\sqrt{y+1}=-\sqrt{x-1}+8$$

Square both sides of the equation.

$$y+1=\left(-\sqrt{x-1}+8\right)^{2}$$

Subtract 1 from both sides of the equation.

$$y+1-1=\left(-\sqrt{x-1}+8\right)^{2}-1$$

Subtracting 1 from itself leaves 0.

$$y=\left(-\sqrt{x-1}+8\right)^{2}-1$$

Subtract 1 from \left(8-\sqrt{x-1}\right)^{2}.

$$y=x-16\sqrt{x-1}+62$$

Solve for x (complex solution)

$$x=y-16\sqrt{y+1}+66$$

$$y=63\text{ or }arg(-\sqrt{y+1}+8)<\pi$$

Solve for y (complex solution)

$$y=x-16\sqrt{x-1}+62$$

$$x=65\text{ or }arg(-\sqrt{x-1}+8)<\pi$$