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

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

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Solution Steps

Square both sides of the equation.

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

Calculate -\sqrt{5-2x} to the power of 2 and get \left(\sqrt{5-2x}\right)^{2}.

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

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

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

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

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

Subtract 2x from both sides.

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

Combine -2x and -2x to get -4x.

$$5-4x=-5$$

Subtract 5 from both sides.

$$-4x=-5-5$$

Subtract 5 from -5 to get -10.

$$-4x=-10$$

Divide both sides by -4.

$$x=\frac{-10}{-4}$$

Reduce the fraction \frac{-10}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{2}$$

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

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

Simplify. The value x=\frac{5}{2} satisfies the equation.

$$0=0$$

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

$$x=\frac{5}{2}$$