Solve y=-sqrt{x-3}

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

Solve for x

$$x=y^{2}+3$$

$$y\leq 0$$

Steps for Solving Radical Equations

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

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide y by -1.

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

Square both sides of the equation.

$$x-3=y^{2}$$

Add 3 to both sides of the equation.

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

Subtracting -3 from itself leaves 0.

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

Subtract -3 from y^{2}.

$$x=y^{2}+3$$

Solve for x (complex solution)

$$x=y^{2}+3$$

$$arg(y)\geq \pi \text{ or }y=0$$

Solve for y

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

$$x\geq 3$$