1. Stating the problem: Solve the equation $$(2x - 5)^2 = -9$$. 2. Analyze the equation: The left side is a square of a real expression, which is always non-negative. The right side is $-9$, which is negative. 3. Since squares of real numbers cannot be negative, there is no real solution to the equation. 4. Conclusion: The equation has \textbf{no real solutions} because $$(2x - 5)^2 \geq 0$$ for all real $x$, but the right side is $-9 < 0$. Final answer: \boxed{\text{No real solution}}