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

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

Solve for x

$$x=2$$

Solution Steps

Square both sides of the equation.

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

Calculate \sqrt{4x-6} to the power of 2 and get 4x-6.

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

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

$$4x-6=x$$

Subtract x from both sides.

$$4x-6-x=0$$

Combine 4x and -x to get 3x.

$$3x-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$3x=6$$

Divide both sides by 3.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$

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

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

Simplify. The value x=2 satisfies the equation.

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

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

$$x=2$$