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

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

Solve for x (complex solution)

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

Solution Steps

Square both sides of the equation.

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

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

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

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

$$x-3=2-x$$

Add x to both sides.

$$x-3+x=2$$

Combine x and x to get 2x.

$$2x-3=2$$

Add 3 to both sides.

$$2x=2+3$$

Add 2 and 3 to get 5.

$$2x=5$$

Divide both sides by 2.

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

Substitute \frac{5}{2} for x in the equation \sqrt{x-3}=\sqrt{2-x}.

$$\sqrt{\frac{5}{2}-3}=\sqrt{2-\frac{5}{2}}$$

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

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

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

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