1. **State the problem:** Simplify the expression $$\frac{1}{2} \sqrt{2} - \sqrt{2}$$. 2. **Recall the rules:** When subtracting like terms involving square roots, treat the square root part as a common factor. 3. **Factor out $$\sqrt{2}$$:** $$\frac{1}{2} \sqrt{2} - \sqrt{2} = \sqrt{2} \left( \frac{1}{2} - 1 \right)$$ 4. **Simplify inside the parentheses:** $$\frac{1}{2} - 1 = \frac{1}{2} - \frac{2}{2} = -\frac{1}{2}$$ 5. **Multiply:** $$\sqrt{2} \times -\frac{1}{2} = -\frac{\sqrt{2}}{2}$$ 6. **Final answer:** $$-\frac{\sqrt{2}}{2}$$ This means the simplified form of the expression is $$-\frac{\sqrt{2}}{2}$$.