The given equation is a quadratic equation:

\[
x^2 + 12x + 36 = 0
\]

To solve it, we can either factor the quadratic expression or use the quadratic formula. Let's start by factoring.

### Factoring the Quadratic Expression:

1. Notice that the equation is a perfect square trinomial. It can be factored as:

\[
(x + 6)(x + 6) = 0
\]

This simplifies to:

\[
(x + 6)^2 = 0
\]

2. To find the solution, set \( x + 6 = 0 \):

\[
x + 6 = 0 \implies x = -6
\]

### Conclusion:
The solution to the equation \(x^2 + 12x + 36 = 0\) is:

\[
x = -6
\]

Would you like a more detailed explanation or have any questions? Here are some related questions:

1. How do you solve a quadratic equation using the quadratic formula?
2. What is a perfect square trinomial?
3. Can quadratic equations have more than one solution?
4. How do you complete the square to solve a quadratic equation?
5. How do you solve quadratic equations by factoring when they are not perfect squares?

**Tip:** Always check if a quadratic equation can be factored easily before applying the quadratic formula; it can save time!

Learn how to solve the quadratic equation x^2 + 12x + 36 = 0 with a detailed step-by-step solution. This problem involves factoring a perfect square trinomial and finding the roots using basic algebraic techniques. Suitable for students in Grades 7-9.

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