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

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

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Solution Steps

Subtract -\sqrt{2x} from both sides of the equation.

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

Square both sides of the equation.

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

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

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

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

$$5-x=2x$$

Subtract 2x from both sides.

$$5-x-2x=0$$

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

$$5-3x=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-5$$

Divide both sides by -3.

$$x=\frac{-5}{-3}$$

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{3}$$

Substitute \frac{5}{3} for x in the equation \sqrt{5-x}-\sqrt{2x}=0.

$$\sqrt{5-\frac{5}{3}}-\sqrt{2\times \frac{5}{3}}=0$$

Simplify. The value x=\frac{5}{3} satisfies the equation.

$$0=0$$

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

$$x=\frac{5}{3}$$