Solve y=2-sqrt{x+7}

$$y = 2 - \sqrt { x + 7 }$$

Solve for x

$$x=\left(2-y\right)^{2}-7$$

$$2-y\geq 0$$

Steps for Solving Radical Equations

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

$$2-\sqrt{x+7}=y$$

Subtract 2 from both sides.

$$-\sqrt{x+7}=y-2$$

Divide both sides by -1.

$$\frac{-\sqrt{x+7}}{-1}=\frac{y-2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{x+7}=\frac{y-2}{-1}$$

Divide y-2 by -1.

$$\sqrt{x+7}=2-y$$

Square both sides of the equation.

$$x+7=\left(2-y\right)^{2}$$

Subtract 7 from both sides of the equation.

$$x+7-7=\left(2-y\right)^{2}-7$$

Subtracting 7 from itself leaves 0.

$$x=\left(2-y\right)^{2}-7$$

Solve for x (complex solution)

$$x=\left(2-y\right)^{2}-7$$

$$y=2\text{ or }arg(2-y)<\pi$$

Solve for y (complex solution)

$$y=-\sqrt{x+7}+2$$

Solve for y

$$y=-\sqrt{x+7}+2$$

$$x\geq -7$$