It looks like there may have been a small typo in the equation you've provided. Assuming you meant to write \(x^2 + 8x + 16 = 0\), I will solve this quadratic equation. If that was not the intended equation, please let me know!

To solve the quadratic equation \(x^2 + 8x + 16 = 0\), we can use the factoring method:

1. **Rewrite the equation:**

   \[
   x^2 + 8x + 16 = 0
   \]

2. **Factor the quadratic expression:**

   We need to find two numbers that multiply to \(16\) (the constant term) and add up to \(8\) (the coefficient of \(x\)). Both numbers are \(4\) because:

   \[
   4 \times 4 = 16 \quad \text{and} \quad 4 + 4 = 8
   \]

   So, we can factor the quadratic as:

   \[
   x^2 + 8x + 16 = (x + 4)(x + 4) = (x + 4)^2
   \]

3. **Set the factor equal to zero to solve for \(x\):**

   \[
   (x + 4)^2 = 0
   \]

   This implies:

   \[
   x + 4 = 0 \quad \Rightarrow \quad x = -4
   \]

Since the factor is repeated, \(x = -4\) is the only solution, also known as a double root.

### Solution:
\[
x = -4
\]

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. What is the meaning of a double root in a quadratic equation?
2. How do you complete the square to solve a quadratic equation?
3. Can a quadratic equation have more than one double root?
4. How does the graph of a quadratic function look when it has a double root?
5. How can you use the discriminant to determine the number of real solutions of a quadratic equation?

**Tip:** The discriminant (\(b^2 - 4ac\)) helps in identifying the nature of roots. If it equals zero, the quadratic has a double root (one real solution).

Learn how to solve the quadratic equation x^2 + 8x + 16 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic equations and using the zero-product property theorem. Suitable for students in Grades 7-9.

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