To solve the quadratic equation \( 2x^2 + 6x - 8 = 0 \), we can use the **quadratic formula**:

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

For this equation, \( a = 2 \), \( b = 6 \), and \( c = -8 \).

### Step-by-step solution:

1. **Calculate the discriminant**:
   \[
   \Delta = b^2 - 4ac = 6^2 - 4(2)(-8) = 36 + 64 = 100
   \]
   So, the discriminant is \( \Delta = 100 \).

2. **Apply the quadratic formula**:
   \[
   x = \frac{-6 \pm \sqrt{100}}{2(2)} = \frac{-6 \pm 10}{4}
   \]

3. **Solve for both values of \( x \)**:
   - For the positive root:
     \[
     x = \frac{-6 + 10}{4} = \frac{4}{4} = 1
     \]
   - For the negative root:
     \[
     x = \frac{-6 - 10}{4} = \frac{-16}{4} = -4
     \]

### Final solution:
The two solutions are:
\[
x = 1 \quad \text{or} \quad x = -4
\]

Would you like any further details or explanations?

---

Here are 5 related questions to consider:
1. How would the solution change if the discriminant was negative?
2. Can you factor \( 2x^2 + 6x - 8 \) directly?
3. What is the significance of the discriminant in determining the type of roots?
4. How would the quadratic formula work if one of the coefficients was 0?
5. What are the steps for completing the square for this equation?

**Tip**: Always check if you can factor a quadratic equation before applying the quadratic formula! It can save time.

Learn how to solve the quadratic equation 2x^2 + 6x - 8 = 0 with a step-by-step explanation using the quadratic formula. This problem covers key algebraic concepts such as calculating the discriminant and applying the quadratic formula. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation