To solve the equation \( x^2 + 10x + 25 = 0 \), we can use the method of factoring, as this is a perfect square trinomial.

### Step-by-Step Solution:

1. **Identify the form of the trinomial**:
   The equation is in the form \( x^2 + 2 \cdot 5 \cdot x + 5^2 = 0 \), which resembles the perfect square \( (x + 5)^2 \).

2. **Rewrite the equation**:
   \[
   x^2 + 10x + 25 = (x + 5)^2
   \]

3. **Set the factored expression equal to zero**:
   \[
   (x + 5)^2 = 0
   \]

4. **Solve for \( x \)**:
   Take the square root of both sides to isolate \( x \):
   \[
   x + 5 = 0
   \]
   \[
   x = -5
   \]

### Final Answer:
The solution is \( x = -5 \).

Would you like more details on factoring or have any questions?

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**Further Practice Questions:**

1. Solve \( x^2 + 12x + 36 = 0 \).
2. Solve \( x^2 - 14x + 49 = 0 \).
3. Factor and solve \( x^2 + 6x + 9 = 0 \).
4. Use the quadratic formula to solve \( x^2 + 10x + 25 = 0 \) and confirm the solution.
5. Solve \( x^2 + 8x + 16 = 0 \) by factoring.

**Tip:** When solving quadratic equations, check if the equation can be factored as a perfect square—it often simplifies the process.

Learn how to solve the quadratic equation x^2 + 10x + 25 = 0 using factoring. This problem demonstrates key algebraic techniques, including recognizing and factoring perfect square trinomials, and applying the zero product property. Ideal for students in Grades 8-10.

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