The given quadratic equation is:

\[
x^2 + 8x + 9 = 0
\]

To solve using the quadratic formula, we use the standard form of a quadratic equation:

\[
ax^2 + bx + c = 0
\]

Here, \(a = 1\), \(b = 8\), and \(c = 9\). The quadratic formula is:

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

Now, let's apply the values:

\[
x = \frac{-8 \pm \sqrt{8^2 - 4(1)(9)}}{2(1)}
\]

Simplifying inside the square root:

\[
x = \frac{-8 \pm \sqrt{64 - 36}}{2}
\]
\[
x = \frac{-8 \pm \sqrt{28}}{2}
\]

Since \(\sqrt{28} = 2\sqrt{7}\), we simplify further:

\[
x = \frac{-8 \pm 2\sqrt{7}}{2}
\]
\[
x = -4 \pm \sqrt{7}
\]

Thus, the two solutions are:

\[
x = -4 + \sqrt{7} \quad \text{or} \quad x = -4 - \sqrt{7}
\]

Would you like more details on any step?

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Here are 5 related questions:
1. How do you derive the quadratic formula?
2. Can you solve \(x^2 + 6x + 8 = 0\) using the quadratic formula?
3. What is the significance of the discriminant \(b^2 - 4ac\) in the quadratic formula?
4. How do you factorize \(x^2 + 8x + 9\) instead of using the quadratic formula?
5. Can you explain how the quadratic formula applies to real-world problems?

**Tip:** Always check the discriminant to know if your solutions will be real or complex!

Learn how to solve the quadratic equation x^2 + 8x + 9 using the quadratic formula. Follow a step-by-step breakdown, covering key algebraic concepts and the application of the quadratic formula. Ideal for students in Grades 8-10.

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