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

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

where \( a = 2 \), \( b = 3 \), and \( c = -2 \).

### Step 1: Identify the coefficients
\[
a = 2, \quad b = 3, \quad c = -2
\]

### Step 2: Calculate the discriminant (\( D \))
\[
D = b^2 - 4ac = 3^2 - 4(2)(-2) = 9 + 16 = 25
\]

### Step 3: Apply the quadratic formula
\[
x = \frac{-3 \pm \sqrt{25}}{2(2)}
\]
\[
x = \frac{-3 \pm 5}{4}
\]

### Step 4: Solve for the two possible values of \( x \)

1. \( x_1 = \frac{-3 + 5}{4} = \frac{2}{4} = \frac{1}{2} \)
2. \( x_2 = \frac{-3 - 5}{4} = \frac{-8}{4} = -2 \)

### Final Solution
The solutions are:
\[
x = \frac{1}{2} \quad \text{or} \quad x = -2
\]

Would you like any further details or have any questions?

Here are 5 related questions:
1. What are the steps involved in using the quadratic formula?
2. How can you determine the number of solutions for a quadratic equation using the discriminant?
3. Can you solve a quadratic equation by factoring instead of using the quadratic formula?
4. How do you graph the equation \( 2x^2 + 3x - 2 = 0 \)?
5. What happens if the discriminant is negative?

**Tip:** Always check if a quadratic equation can be factored easily before using the quadratic formula; it might save you time!

Learn how to solve the quadratic equation 2x^2 + 3x - 2 using the quadratic formula. This detailed step-by-step guide walks through solving for x by calculating the discriminant and applying the quadratic equation formula. Suitable for students in Grades 9-12.

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