The given quadratic equation is:

\[
2x^2 - 17x - 30 = 0
\]

To solve this, we'll use the **quadratic formula**:

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

In this case, the coefficients are:
- \( a = 2 \)
- \( b = -17 \)
- \( c = -30 \)

### Step 1: Calculate the discriminant (\( \Delta \))
\[
\Delta = b^2 - 4ac = (-17)^2 - 4(2)(-30) = 289 + 240 = 529
\]

### Step 2: Use the quadratic formula
\[
x = \frac{-(-17) \pm \sqrt{529}}{2(2)}
\]
\[
x = \frac{17 \pm 23}{4}
\]

### Step 3: Solve for \( x \)
Now, solve for the two values of \( x \):

1. \( x_1 = \frac{17 + 23}{4} = \frac{40}{4} = 10 \)
2. \( x_2 = \frac{17 - 23}{4} = \frac{-6}{4} = -\frac{3}{2} \)

### Final Answer:
\[
x_1 = 10, \quad x_2 = -\frac{3}{2}
\]

Let me know if you'd like more details or clarifications!

---

Here are 5 related questions to expand on this:

1. How do you factor quadratic equations manually?
2. What is the significance of the discriminant in the quadratic formula?
3. Can you use completing the square to solve the same equation?
4. How do you solve quadratic equations graphically?
5. How does the quadratic formula apply to real-world problems?

**Tip:** Always check the discriminant before solving; it tells you the nature of the roots (real, complex, or repeated).

Learn how to solve the quadratic equation 2x^2 - 17x - 30 using the quadratic formula. This detailed guide includes key algebraic concepts such as the discriminant and provides a step-by-step solution for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation