Solve y=-1/2sqrt{x+2}+4

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

Solve for x

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

$$8-2y\geq 0$$

Steps for Solving Radical Equations

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

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

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

Subtract 4 from both sides.

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

Multiply both sides by -2.

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

Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.

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

Divide y-4 by -\frac{1}{2} by multiplying y-4 by the reciprocal of -\frac{1}{2}.

$$\sqrt{x+2}=8-2y$$

Square both sides of the equation.

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

Subtract 2 from both sides of the equation.

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

Subtracting 2 from itself leaves 0.

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

Solve for x (complex solution)

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

$$y=4\text{ or }arg(8-2y)<\pi$$

Solve for y (complex solution)

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

Solve for y

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

$$x\geq -2$$