To solve the equation $x^2 + 2x + 1 = 4$ by completing the square, let's go through the steps:

1. Rewrite the equation: $x^2 + 2x + 1 = 4$

2. Recognize that $x^2 + 2x + 1$ is a perfect square trinomial: $(x + 1)^2 = 4$

3. Rewrite the equation using the perfect square form: $(x + 1)^2 = 4$

4. Take the square root of both sides: $x + 1 = \pm 2$

5. Solve for $x$ by isolating it in each case:

   • For $x + 1 = 2$: $x = 2 - 1 = 1$
   • For $x + 1 = -2$: $x = -2 - 1 = -3$

6. Final answer: The solutions are $x = -3$ and $x = 1$.

Since the prompt asks for the smallest amount first, the answer should be entered as: $x = [-3, 1]$

Would you like further details or have any questions?

Here are some related questions to further explore the topic:

1. What is the process of completing the square, and when is it used?
2. Can all quadratic equations be solved by completing the square?
3. How does completing the square help in deriving the quadratic formula?
4. What are the other methods for solving quadratic equations?
5. How would the approach change if the equation had a negative or fractional coefficient?

Tip: When completing the square, always check if the equation can be simplified into a perfect square trinomial, which makes the process easier.