https://file.aiquickdraw.com/mathbot/file/1725483176419v5cfn5x5.jpg

The equation in the image is:

\[
x^2 + 10x + 9 = 0
\]

To solve this quadratic equation, we can use the quadratic formula:

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

Here, the coefficients are:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = 10 \) (coefficient of \( x \))
- \( c = 9 \) (constant term)

Let's calculate the discriminant and then the roots.

1. **Discriminant:**
   \[
   \text{Discriminant} = b^2 - 4ac = 10^2 - 4(1)(9) = 100 - 36 = 64
   \]

2. **Roots:**
   \[
   x = \frac{-10 \pm \sqrt{64}}{2(1)} = \frac{-10 \pm 8}{2}
   \]

   - For \( x_1 \):
     \[
     x_1 = \frac{-10 + 8}{2} = \frac{-2}{2} = -1
     \]
   - For \( x_2 \):
     \[
     x_2 = \frac{-10 - 8}{2} = \frac{-18}{2} = -9
     \]

So, the solutions are:

\[
x_1 = -1 \quad \text{and} \quad x_2 = -9
\]

Would you like more details on this process, or do you have any questions?

---

Here are some related questions you might find interesting:

1. How does the discriminant help determine the nature of the roots?
2. What are some methods to solve quadratic equations other than using the quadratic formula?
3. How can quadratic equations be used to model real-world situations?
4. What does it mean when the discriminant is negative, zero, or positive?
5. How can you factor quadratic equations that do not have rational roots?

**Tip:** When solving quadratic equations, always check if the equation can be factored easily before using the quadratic formula—it can save time!

Solve the quadratic equation x^2 + 10x + 9 = 0.

Learn how to solve the quadratic equation x^2 + 10x + 9 with a step-by-step approach using the quadratic formula. This tutorial is perfect for students in Grades 8-10 and covers the application of the discriminant to determine the nature of the roots.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation