Solve 2sqrt{-(x-5)}+3=y

$$2 \sqrt { - ( x - 5 ) } + 3 = y$$

Solve for x

$$x=-\frac{\left(3-y\right)^{2}}{4}+5$$

$$\frac{y-3}{2}\geq 0$$

Steps for Solving Radical Equations

To find the opposite of x-5, find the opposite of each term.

$$2\sqrt{-x+5}+3=y$$

Subtract 3 from both sides.

$$2\sqrt{-x+5}=y-3$$

Divide both sides by 2.

$$\frac{2\sqrt{-x+5}}{2}=\frac{y-3}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\sqrt{-x+5}=\frac{y-3}{2}$$

Square both sides of the equation.

$$-x+5=\frac{\left(y-3\right)^{2}}{4}$$

Subtract 5 from both sides of the equation.

$$-x+5-5=\frac{\left(y-3\right)^{2}}{4}-5$$

Subtracting 5 from itself leaves 0.

$$-x=\frac{\left(y-3\right)^{2}}{4}-5$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\frac{\left(y-3\right)^{2}}{4}-5}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\frac{\left(y-3\right)^{2}}{4}-5}{-1}$$

Divide \frac{\left(y-3\right)^{2}}{4}-5 by -1.

$$x=-\frac{\left(y-3\right)^{2}}{4}+5$$

Solve for x (complex solution)

$$x=-\frac{\left(3-y\right)^{2}}{4}+5$$

$$y=3\text{ or }arg(\frac{3-y}{2})\geq \pi$$

Solve for y (complex solution)

$$y=2\sqrt{5-x}+3$$

Solve for y

$$y=2\sqrt{5-x}+3$$

$$x\leq 5$$