Solve 2=5-sqrt{2x+4}

$$2=5- \sqrt{ 2x+4 }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Radical Equations

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

$$5-\sqrt{2x+4}=2$$

Subtract 5 from both sides.

$$-\sqrt{2x+4}=2-5$$

Subtract 5 from 2 to get -3.

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

Divide both sides by -1.

$$\sqrt{2x+4}=\frac{-3}{-1}$$

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$\sqrt{2x+4}=3$$

Square both sides of the equation.

$$2x+4=9$$

Subtract 4 from both sides of the equation.

$$2x+4-4=9-4$$

Subtracting 4 from itself leaves 0.

$$2x=9-4$$

Subtract 4 from 9.

$$2x=5$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{5}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{5}{2}$$