Solve y=1-2sqrt{x+3}

$$y = 1 - 2 \sqrt { x + 3 }$$

Solve for x

$$x=\frac{\left(1-y\right)^{2}-12}{4}$$

$$\frac{1-y}{2}\geq 0$$

Steps for Solving Radical Equations

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

$$1-2\sqrt{x+3}=y$$

Subtract 1 from both sides.

$$-2\sqrt{x+3}=y-1$$

Divide both sides by -2.

$$\frac{-2\sqrt{x+3}}{-2}=\frac{y-1}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$\sqrt{x+3}=\frac{y-1}{-2}$$

Divide y-1 by -2.

$$\sqrt{x+3}=\frac{1-y}{2}$$

Square both sides of the equation.

$$x+3=\frac{\left(1-y\right)^{2}}{4}$$

Subtract 3 from both sides of the equation.

$$x+3-3=\frac{\left(1-y\right)^{2}}{4}-3$$

Subtracting 3 from itself leaves 0.

$$x=\frac{\left(1-y\right)^{2}}{4}-3$$

Solve for x (complex solution)

$$x=\frac{\left(1-y\right)^{2}-12}{4}$$

$$y=1\text{ or }arg(\frac{1-y}{2})<\pi$$

Solve for y (complex solution)

$$y=-2\sqrt{x+3}+1$$

Solve for y

$$y=-2\sqrt{x+3}+1$$

$$x\geq -3$$