Solve sqrt{x+3}=sqrt{2x-3}

$$\sqrt { x + 3 } = \sqrt { 2 x - 3 }$$

Solve for x

$$x=6$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x+3}\right)^{2}=\left(\sqrt{2x-3}\right)^{2}$$

Calculate \sqrt{x+3} to the power of 2 and get x+3.

$$x+3=\left(\sqrt{2x-3}\right)^{2}$$

Calculate \sqrt{2x-3} to the power of 2 and get 2x-3.

$$x+3=2x-3$$

Subtract 2x from both sides.

$$x+3-2x=-3$$

Combine x and -2x to get -x.

$$-x+3=-3$$

Subtract 3 from both sides.

$$-x=-3-3$$

Subtract 3 from -3 to get -6.

$$-x=-6$$

Multiply both sides by -1.

$$x=6$$

Substitute 6 for x in the equation \sqrt{x+3}=\sqrt{2x-3}.

$$\sqrt{6+3}=\sqrt{2\times 6-3}$$

Simplify. The value x=6 satisfies the equation.

$$3=3$$

Equation \sqrt{x+3}=\sqrt{2x-3} has a unique solution.

$$x=6$$