Solve sqrt{2x-6}=sqrt{x-4}

$$\sqrt{ 2x-6 } = \sqrt{ x-4 }$$

Solve for x (complex solution)

$$x=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2x-6}\right)^{2}=\left(\sqrt{x-4}\right)^{2}$$

Calculate \sqrt{2x-6} to the power of 2 and get 2x-6.

$$2x-6=\left(\sqrt{x-4}\right)^{2}$$

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

$$2x-6=x-4$$

Subtract x from both sides.

$$2x-6-x=-4$$

Combine 2x and -x to get x.

$$x-6=-4$$

Add 6 to both sides.

$$x=-4+6$$

Add -4 and 6 to get 2.

$$x=2$$

Substitute 2 for x in the equation \sqrt{2x-6}=\sqrt{x-4}.

$$\sqrt{2\times 2-6}=\sqrt{2-4}$$

Simplify. The value x=2 satisfies the equation.

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

Equation \sqrt{2x-6}=\sqrt{x-4} has a unique solution.

$$x=2$$