Solve sqrt{2x-1}-sqrt{x+4}=0

$$\sqrt { 2 x - 1 } - \sqrt { x + 4 } = 0$$

Solve for x

$$x=5$$

Solution Steps

Subtract -\sqrt{x+4} from both sides of the equation.

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

Square both sides of the equation.

$$\left(\sqrt{2x-1}\right)^{2}=\left(\sqrt{x+4}\right)^{2}$$

Calculate \sqrt{2x-1} to the power of 2 and get 2x-1.

$$2x-1=\left(\sqrt{x+4}\right)^{2}$$

Calculate \sqrt{x+4} to the power of 2 and get x+4.

$$2x-1=x+4$$

Subtract x from both sides.

$$2x-1-x=4$$

Combine 2x and -x to get x.

$$x-1=4$$

Add 1 to both sides.

$$x=4+1$$

Add 4 and 1 to get 5.

$$x=5$$

Substitute 5 for x in the equation \sqrt{2x-1}-\sqrt{x+4}=0.

$$\sqrt{2\times 5-1}-\sqrt{5+4}=0$$

Simplify. The value x=5 satisfies the equation.

$$0=0$$

Equation \sqrt{2x-1}=\sqrt{x+4} has a unique solution.

$$x=5$$