Solve y=sqrt{-x}+3

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

Solve for x

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

$$-\left(3-y\right)\geq 0$$

Steps for Solving Radical Equations

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

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

Subtract 3 from both sides.

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

Square both sides of the equation.

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

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\left(y-3\right)^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\left(y-3\right)^{2}}{-1}$$

Divide \left(y-3\right)^{2} by -1.

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

Solve for x (complex solution)

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

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

Solve for y

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

$$x\leq 0$$