To solve the quadratic equation \(x^2 + 12x + 27 = 0\), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this equation, \(a = 1\), \(b = 12\), and \(c = 27\).

1. **Calculate the discriminant:**

\[
\text{Discriminant} = b^2 - 4ac = 12^2 - 4(1)(27) = 144 - 108 = 36
\]

2. **Calculate the roots:**

\[
x = \frac{-12 \pm \sqrt{36}}{2(1)} = \frac{-12 \pm 6}{2}
\]

This gives us two possible solutions:

\[
x_1 = \frac{-12 + 6}{2} = \frac{-6}{2} = -3
\]

\[
x_2 = \frac{-12 - 6}{2} = \frac{-18}{2} = -9
\]

So, the solutions are \(x = -3\) and \(x = -9\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the solution change if the constant term was different, e.g., \(x^2 + 12x + 36 = 0\)?
2. What happens if the discriminant is negative in a quadratic equation?
3. Can you factor the quadratic equation \(x^2 + 12x + 27\) to find the roots?
4. How can you derive the quadratic formula from completing the square?
5. What is the significance of the discriminant in determining the nature of the roots?

**Tip:** Always check the discriminant first in a quadratic equation. It tells you whether you'll have real or complex roots and how many roots there are.

Learn how to solve the quadratic equation x^2 + 12x + 27 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula and discriminant. Suitable for students in Grades 7-9.

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