Solve sqrt{28+6}-sqrt{x-4}=3

$$\sqrt { 28 + 6 } - \sqrt { x - 4 } = 3$$

Solve for x

$$x=47-6\sqrt{34}\approx 12.014288631$$

Steps for Solving Radical Equations

Subtract \sqrt{34} from both sides of the equation.

$$-\sqrt{x-4}+\sqrt{34}-\sqrt{34}=3-\sqrt{34}$$

Subtracting \sqrt{34} from itself leaves 0.

$$-\sqrt{x-4}=3-\sqrt{34}$$

Divide both sides by -1.

$$\frac{-\sqrt{x-4}}{-1}=\frac{3-\sqrt{34}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{x-4}=\frac{3-\sqrt{34}}{-1}$$

Divide 3-\sqrt{34} by -1.

$$\sqrt{x-4}=\sqrt{34}-3$$

Square both sides of the equation.

$$x-4=43-6\sqrt{34}$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=43-6\sqrt{34}-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=43-6\sqrt{34}-\left(-4\right)$$

Subtract -4 from 43-6\sqrt{34}.

$$x=47-6\sqrt{34}$$