Solve the quadratic equation.
2x2+5x–8=0

The quadratic equation is:

\[
2x^2 + 5x - 8 = 0
\]

We can solve this using the quadratic formula:

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

For the given equation \(2x^2 + 5x - 8 = 0\), the coefficients are:
- \(a = 2\)
- \(b = 5\)
- \(c = -8\)

### Step 1: Calculate the discriminant
The discriminant is:

\[
\Delta = b^2 - 4ac = 5^2 - 4(2)(-8) = 25 + 64 = 89
\]

### Step 2: Apply the quadratic formula

\[
x = \frac{-5 \pm \sqrt{89}}{2(2)} = \frac{-5 \pm \sqrt{89}}{4}
\]

### Step 3: Simplify the results

The two possible solutions are:

\[
x_1 = \frac{-5 + \sqrt{89}}{4} \quad \text{and} \quad x_2 = \frac{-5 - \sqrt{89}}{4}
\]

Thus, the solutions are:

\[
x_1 \approx 0.611 \quad \text{and} \quad x_2 \approx -3.611
\]

Would you like a deeper explanation, or any questions so far?

Here are 5 related questions you could explore:
1. What is the discriminant, and how does it affect the nature of roots in quadratic equations?
2. How would the solution change if \(a\), \(b\), or \(c\) were different?
3. Can you solve a quadratic equation by factoring instead of using the quadratic formula?
4. What are complex roots, and when do they occur in quadratic equations?
5. How is completing the square used to solve quadratic equations?

**Tip:** Always check the discriminant before solving a quadratic equation, as it reveals important information about the type of solutions you'll get.

Solve the quadratic equation. 2x^2 + 5x - 8 = 0

Explore how to solve the quadratic equation 2x^2 + 5x - 8 using the quadratic formula. This step-by-step solution breaks down key algebraic concepts, such as discriminants and root calculations. Ideal for Grades 9-11 students.

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