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Let's solve the given quadratic equation \(x^2 + 4x + 3 = 0\) by completing the square.

### Step-by-step solution:

1. **Move the constant to the other side**:
   \[
   x^2 + 4x = -3
   \]

2. **Complete the square**: 
   To complete the square, take half of the coefficient of \(x\), which is 4. Half of 4 is 2, and then square it to get \(2^2 = 4\). Now, add 4 to both sides of the equation:
   \[
   x^2 + 4x + 4 = -3 + 4
   \]
   \[
   (x + 2)^2 = 1
   \]

3. **Solve for \(x\)**:
   Take the square root of both sides:
   \[
   x + 2 = \pm 1
   \]
   Now, solve for \(x\) by subtracting 2 from both sides:
   \[
   x = -2 \pm 1
   \]
   This gives two solutions:
   \[
   x = -2 + 1 = -1 \quad \text{or} \quad x = -2 - 1 = -3
   \]

### Final answer:
The solutions are \(x = -3\) and \(x = -1\). Since the smallest value should be entered first, the blanks should be:

- \(x = -3, -1\)

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

Here are 5 related questions to explore:
1. How do you complete the square for equations with a leading coefficient other than 1?
2. What is the quadratic formula, and when should it be used?
3. How can you recognize if a quadratic equation is factorable without completing the square?
4. What are some applications of completing the square in geometry or physics?
5. How does completing the square help in deriving the quadratic formula?

**Tip**: Completing the square is also useful in converting quadratic equations into vertex form, which can help identify the vertex of a parabola easily.

Solve the equation x^2 + 4x + 3 = 0 by completing the square.

Learn how to solve the quadratic equation x^2 + 4x + 3 = 0 using the method of completing the square. This tutorial provides a step-by-step guide on how to transform the equation into a perfect square and solve for x, a fundamental algebra skill for students in Grades 9-10.

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