Solve sqrt{2x-8}=sqrt{x+5}

$$\sqrt { 2 x - 8 } = \sqrt { x + 5 }$$

Solve for x

$$x=13$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2x-8}\right)^{2}=\left(\sqrt{x+5}\right)^{2}$$

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

$$2x-8=\left(\sqrt{x+5}\right)^{2}$$

Calculate \sqrt{x+5} to the power of 2 and get x+5.

$$2x-8=x+5$$

Subtract x from both sides.

$$2x-8-x=5$$

Combine 2x and -x to get x.

$$x-8=5$$

Add 8 to both sides.

$$x=5+8$$

Add 5 and 8 to get 13.

$$x=13$$

Substitute 13 for x in the equation \sqrt{2x-8}=\sqrt{x+5}.

$$\sqrt{2\times 13-8}=\sqrt{13+5}$$

Simplify. The value x=13 satisfies the equation.

$$3\times 2^{\frac{1}{2}}=3\times 2^{\frac{1}{2}}$$

Equation \sqrt{2x-8}=\sqrt{x+5} has a unique solution.

$$x=13$$