Let's work on simplifying the expression:

$-\sqrt{50} + 2\sqrt{18}$

Step 1: Simplify $\sqrt{50}$

$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$ Thus, $-\sqrt{50} = -5\sqrt{2}$.

Step 2: Simplify $\sqrt{18}$

$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$ Now, multiply by 2: $2\sqrt{18} = 2 \times 3\sqrt{2} = 6\sqrt{2}$

Step 3: Combine the terms

Now combine $-5\sqrt{2}$ and $6\sqrt{2}$: $-5\sqrt{2} + 6\sqrt{2} = (6 - 5)\sqrt{2} = \sqrt{2}$

Thus, the simplified expression is: $\boxed{\sqrt{2}}$

Would you like more details or have any questions about this process?

Here are some related questions to explore:

1. How do you simplify square roots involving larger numbers?
2. Can all square roots be simplified like this?
3. What is the difference between simplifying and approximating square roots?
4. How would the process change if there were cube roots involved instead of square roots?
5. How do you handle square roots in the denominator when simplifying expressions?

Tip: Always factor numbers inside the square root to find perfect squares for easier simplification.