Solve y=-4-frac{sqrt{16-(x-3)}}{2}

$$y = -4- \frac{ \sqrt{ 16-(x-3) } }{ 2 }$$

Solve for x

$$x=-4\left(y+4\right)^{2}+19$$

$$-\left(2y+8\right)\geq 0$$

Steps for Solving Radical Equations

To find the opposite of x-3, find the opposite of each term.

$$y=-4-\frac{\sqrt{16-x+3}}{2}$$

Add 16 and 3 to get 19.

$$y=-4-\frac{\sqrt{19-x}}{2}$$

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

$$-4-\frac{\sqrt{19-x}}{2}=y$$

Add 4 to both sides.

$$-\frac{\sqrt{19-x}}{2}=y+4$$

Multiply both sides of the equation by 2.

$$-\sqrt{19-x}=2y+8$$

Divide both sides by -1.

$$\frac{-\sqrt{-x+19}}{-1}=\frac{2y+8}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{-x+19}=\frac{2y+8}{-1}$$

Divide 8+2y by -1.

$$\sqrt{-x+19}=-2y-8$$

Square both sides of the equation.

$$-x+19=4\left(y+4\right)^{2}$$

Subtract 19 from both sides of the equation.

$$-x+19-19=4\left(y+4\right)^{2}-19$$

Subtracting 19 from itself leaves 0.

$$-x=4\left(y+4\right)^{2}-19$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{4\left(y+4\right)^{2}-19}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{4\left(y+4\right)^{2}-19}{-1}$$

Divide 4\left(4+y\right)^{2}-19 by -1.

$$x=-4\left(y+4\right)^{2}+19$$

Solve for x (complex solution)

$$x=-4\left(y+4\right)^{2}+19$$

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

Solve for y (complex solution)

$$y=-\frac{\sqrt{19-x}}{2}-4$$

Solve for y

$$y=-\frac{\sqrt{19-x}}{2}-4$$

$$x\leq 19$$