To solve the quadratic equation \( x^2 + 3x - 8 = 0 \), we can use the quadratic formula:

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

Here, \( a = 1 \), \( b = 3 \), and \( c = -8 \).

### Step 1: Calculate the discriminant
\[
\text{Discriminant} = b^2 - 4ac = 3^2 - 4(1)(-8) = 9 + 32 = 41
\]

### Step 2: Apply the quadratic formula
\[
x = \frac{-3 \pm \sqrt{41}}{2(1)} = \frac{-3 \pm \sqrt{41}}{2}
\]

### Step 3: Write the solutions
The solutions are:
\[
x_1 = \frac{-3 + \sqrt{41}}{2}
\]
\[
x_2 = \frac{-3 - \sqrt{41}}{2}
\]

These are the exact solutions. If you need approximate values, they are:
\[
x_1 \approx 2.70
\]
\[
x_2 \approx -5.70
\]

Would you like more details or have any questions?

---

Here are 5 related questions you might find interesting:
1. What are the steps to derive the quadratic formula?
2. How does the discriminant determine the nature of the roots?
3. Can you solve the quadratic equation \( x^2 + 5x + 6 = 0 \)?
4. What happens when the discriminant is zero?
5. How do you complete the square to solve a quadratic equation?

**Tip:** Always check the discriminant first; it helps you predict the nature of the roots!

Learn how to solve the quadratic equation x^2 + 3x - 8 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula and discriminant calculation. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation