Solve y=-2/2sqrt{x+2}+4

$$y = \frac { - 2 } { 2 } \sqrt { x + 2 } + 4$$

Solve for x

$$x=\left(4-y\right)^{2}-2$$

$$4-y\geq 0$$

Steps for Solving Radical Equations

Divide -2 by 2 to get -1.

$$y=-\sqrt{x+2}+4$$

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

$$-\sqrt{x+2}+4=y$$

Subtract 4 from both sides.

$$-\sqrt{x+2}=y-4$$

Divide both sides by -1.

$$\frac{-\sqrt{x+2}}{-1}=\frac{y-4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{x+2}=\frac{y-4}{-1}$$

Divide y-4 by -1.

$$\sqrt{x+2}=4-y$$

Square both sides of the equation.

$$x+2=\left(4-y\right)^{2}$$

Subtract 2 from both sides of the equation.

$$x+2-2=\left(4-y\right)^{2}-2$$

Subtracting 2 from itself leaves 0.

$$x=\left(4-y\right)^{2}-2$$

Solve for x (complex solution)

$$x=\left(4-y\right)^{2}-2$$

$$y=4\text{ or }arg(4-y)<\pi$$

Solve for y (complex solution)

$$y=-\sqrt{x+2}+4$$

Solve for y

$$y=-\sqrt{x+2}+4$$

$$x\geq -2$$