Solve sqrt{x-8}=sqrt{3x-34}

$$\sqrt { x - 8 } = \sqrt { 3 x - 34 }$$

Solve for x

$$x=13$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x-8}\right)^{2}=\left(\sqrt{3x-34}\right)^{2}$$

Calculate \sqrt{x-8} to the power of 2 and get x-8.

$$x-8=\left(\sqrt{3x-34}\right)^{2}$$

Calculate \sqrt{3x-34} to the power of 2 and get 3x-34.

$$x-8=3x-34$$

Subtract 3x from both sides.

$$x-8-3x=-34$$

Combine x and -3x to get -2x.

$$-2x-8=-34$$

Add 8 to both sides.

$$-2x=-34+8$$

Add -34 and 8 to get -26.

$$-2x=-26$$

Divide both sides by -2.

$$x=\frac{-26}{-2}$$

Divide -26 by -2 to get 13.

$$x=13$$

Substitute 13 for x in the equation \sqrt{x-8}=\sqrt{3x-34}.

$$\sqrt{13-8}=\sqrt{3\times 13-34}$$

Simplify. The value x=13 satisfies the equation.

$$5^{\frac{1}{2}}=5^{\frac{1}{2}}$$

Equation \sqrt{x-8}=\sqrt{3x-34} has a unique solution.

$$x=13$$