Solve y=2-sqrt{5-x}

$$y = 2 - \sqrt { 5 - x }$$

Solve for x

$$x=-\left(2-y\right)^{2}+5$$

$$2-y\geq 0$$

Steps for Solving Radical Equations

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

$$2-\sqrt{5-x}=y$$

Subtract 2 from both sides.

$$-\sqrt{5-x}=y-2$$

Divide both sides by -1.

$$\frac{-\sqrt{-x+5}}{-1}=\frac{y-2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{-x+5}=\frac{y-2}{-1}$$

Divide y-2 by -1.

$$\sqrt{-x+5}=2-y$$

Square both sides of the equation.

$$-x+5=\left(2-y\right)^{2}$$

Subtract 5 from both sides of the equation.

$$-x+5-5=\left(2-y\right)^{2}-5$$

Subtracting 5 from itself leaves 0.

$$-x=\left(2-y\right)^{2}-5$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\left(2-y\right)^{2}-5}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\left(2-y\right)^{2}-5}{-1}$$

Divide \left(-y+2\right)^{2}-5 by -1.

$$x=-\left(2-y\right)^{2}+5$$

Solve for x (complex solution)

$$x=-\left(2-y\right)^{2}+5$$

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

Solve for y (complex solution)

$$y=-\sqrt{5-x}+2$$

Solve for y

$$y=-\sqrt{5-x}+2$$

$$x\leq 5$$