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

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

Solve for x

$$x=-\frac{\left(2-y\right)\left(y-6\right)}{4}$$

$$-\frac{y}{2}+2\geq 0$$

Steps for Solving Radical Equations

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

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

Subtract 4 from both sides.

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

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

Divide y-4 by -2.

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

Square both sides of the equation.

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

Subtract 1 from both sides of the equation.

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

Subtracting 1 from itself leaves 0.

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

Subtract 1 from \frac{\left(-y+4\right)^{2}}{4}.

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

Solve for x (complex solution)

$$x=-\frac{\left(2-y\right)\left(y-6\right)}{4}$$

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

Solve for y (complex solution)

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

Solve for y

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

$$x\geq -1$$