https://file.aiquickdraw.com/mathbot/file/1725426025809rcjf1626.jpg

The equation provided in the image is:

\[ x^2 + 2x + 1 = 0 \]

This is a quadratic equation in the form \( ax^2 + bx + c = 0 \) where \( a = 1 \), \( b = 2 \), and \( c = 1 \).

### To solve this quadratic equation:
1. **Factorization**: 
   \[
   x^2 + 2x + 1 = (x + 1)(x + 1) = 0
   \]
   This simplifies to:
   \[
   (x + 1)^2 = 0
   \]
   Taking the square root of both sides gives:
   \[
   x + 1 = 0
   \]
   Therefore, the solution is:
   \[
   x = -1
   \]

2. **Verification**:
   Substitute \( x = -1 \) back into the original equation:
   \[
   (-1)^2 + 2(-1) + 1 = 1 - 2 + 1 = 0
   \]
   This confirms that \( x = -1 \) is indeed the correct solution.

### The solution is:
\[
x = -1
\]

Would you like more details or have any questions?

### Related Questions:
1. How would you solve the equation if it wasn't easily factorable?
2. What does the discriminant tell you about the nature of the roots in a quadratic equation?
3. How would the solution change if the equation had no real roots?
4. Can you explain how the quadratic formula derives from completing the square?
5. What is the graphical interpretation of the solution \( x = -1 \)?

**Tip:** Always verify your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Learn how to solve the quadratic equation 5x^2 + 2x + 1 = 0 using the quadratic formula. This step-by-step guide covers essential algebraic concepts, making it ideal for students in Grades 7-9.

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