Solve sqrt{5-2x}-sqrt{9-x}=0

$$\sqrt{ 5-2x } - \sqrt{ 9-x } =0$$

Solve for x

$$x=-4$$

Solution Steps

Subtract -\sqrt{9-x} from both sides of the equation.

$$\sqrt{5-2x}=\sqrt{9-x}$$

Square both sides of the equation.

$$\left(\sqrt{5-2x}\right)^{2}=\left(\sqrt{9-x}\right)^{2}$$

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

$$5-2x=\left(\sqrt{9-x}\right)^{2}$$

Calculate \sqrt{9-x} to the power of 2 and get 9-x.

$$5-2x=9-x$$

Add x to both sides.

$$5-2x+x=9$$

Combine -2x and x to get -x.

$$5-x=9$$

Subtract 5 from both sides.

$$-x=9-5$$

Subtract 5 from 9 to get 4.

$$-x=4$$

Multiply both sides by -1.

$$x=-4$$

Substitute -4 for x in the equation \sqrt{5-2x}-\sqrt{9-x}=0.

$$\sqrt{5-2\left(-4\right)}-\sqrt{9-\left(-4\right)}=0$$

Simplify. The value x=-4 satisfies the equation.

$$0=0$$

Equation \sqrt{5-2x}=\sqrt{9-x} has a unique solution.

$$x=-4$$