Let's break this expression down step by step:

Given expression: $2 + [-2 - 5 \{ 7 + 2(3 + 14) \}]$

Step 1: Simplify the parentheses first.

Inside the innermost parentheses: $3 + 14 = 17$

Now, substitute this back into the expression: $2 + [-2 - 5 \{ 7 + 2(17) \}]$

Step 2: Simplify the multiplication within the brackets.

Multiply $2 \times 17 = 34$, then substitute: $2 + [-2 - 5 \{ 7 + 34 \}]$

Step 3: Add inside the curly brackets.

$7 + 34 = 41$

So, the expression becomes: $2 + [-2 - 5(41)]$

Step 4: Simplify the multiplication.

Multiply $5 \times 41 = 205$, so we get: $2 + [-2 - 205]$

Step 5: Simplify the terms inside the square brackets.

$-2 - 205 = -207$

Thus, the expression is now: $2 + (-207)$

Step 6: Add the final terms.

$2 + (-207) = -205$

Final Answer:

$\boxed{-205}$

Would you like more details on any of the steps, or do you have any questions?

Here are 5 related questions for further practice:

1. Simplify $3 + [-4 - 3\{2 + 5(1 + 2)\}]$.
2. Solve $4 + [1 - 6\{8 + 3(2 + 5)\}]$.
3. Evaluate $2 + [-3 - 4\{6 + 2(7 + 1)\}]$.
4. Calculate $5 + [-1 - 3\{9 + 4(2 + 6)\}]$.
5. Simplify $1 + [-3 - 2\{10 + 2(5 + 4)\}]$.

Tip: Always start simplifying from the innermost parentheses or brackets.