1. **State the problem:** Simplify the expression $$(-5)^2 - 2 \times (-9) + 6$$ using the correct order of operations. 2. **Recall the order of operations:** Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 3. **Evaluate exponents first:** $$(-5)^2 = 25$$. 4. **Multiply:** $$-2 \times (-9) = 18$$. 5. **Substitute back:** $$25 + 18 + 6$$. 6. **Add:** $$25 + 18 = 43$$, then $$43 + 6 = 49$$. **Final answer:** $$49$$.