Solve y=-sqrt{x+5}+3

$$y = - \sqrt { x + 5 } + 3$$

Solve for x

$$x=\left(3-y\right)^{2}-5$$

$$3-y\geq 0$$

Steps for Solving Radical Equations

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

$$-\sqrt{x+5}+3=y$$

Subtract 3 from both sides.

$$-\sqrt{x+5}=y-3$$

Divide both sides by -1.

$$\frac{-\sqrt{x+5}}{-1}=\frac{y-3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{x+5}=\frac{y-3}{-1}$$

Divide y-3 by -1.

$$\sqrt{x+5}=3-y$$

Square both sides of the equation.

$$x+5=\left(3-y\right)^{2}$$

Subtract 5 from both sides of the equation.

$$x+5-5=\left(3-y\right)^{2}-5$$

Subtracting 5 from itself leaves 0.

$$x=\left(3-y\right)^{2}-5$$

Solve for x (complex solution)

$$x=\left(3-y\right)^{2}-5$$

$$y=3\text{ or }arg(3-y)<\pi$$

Solve for y

$$y=-\sqrt{x+5}+3$$

$$x\geq -5$$