Solve sqrt{x-5}=sqrt{2x-7}

$$\sqrt{ x-5 } = \sqrt{ 2x-7 }$$

Solve for x (complex solution)

$$x=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x-5}\right)^{2}=\left(\sqrt{2x-7}\right)^{2}$$

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

$$x-5=\left(\sqrt{2x-7}\right)^{2}$$

Calculate \sqrt{2x-7} to the power of 2 and get 2x-7.

$$x-5=2x-7$$

Subtract 2x from both sides.

$$x-5-2x=-7$$

Combine x and -2x to get -x.

$$-x-5=-7$$

Add 5 to both sides.

$$-x=-7+5$$

Add -7 and 5 to get -2.

$$-x=-2$$

Multiply both sides by -1.

$$x=2$$

Substitute 2 for x in the equation \sqrt{x-5}=\sqrt{2x-7}.

$$\sqrt{2-5}=\sqrt{2\times 2-7}$$

Simplify. The value x=2 satisfies the equation.

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

Equation \sqrt{x-5}=\sqrt{2x-7} has a unique solution.

$$x=2$$