https://file.aiquickdraw.com/mathbot/file/1728929473354okswgyxf.jpg

The image shows a quadratic equation: 

\[
2x^2 + 7x - 2 = 0
\]

It also displays the quadratic formula, which is used to solve for \(x\):

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

For this equation:
- \(a = 2\)
- \(b = 7\)
- \(c = -2\)

Let’s plug these values into the quadratic formula:

1. **Calculate the discriminant** \(b^2 - 4ac\):
   \[
   7^2 - 4(2)(-2) = 49 + 16 = 65
   \]
   So, the discriminant is 65.

2. **Substitute into the formula**:
   \[
   x = \frac{-7 \pm \sqrt{65}}{2(2)}
   \]
   Simplifying:
   \[
   x = \frac{-7 \pm \sqrt{65}}{4}
   \]

Thus, the solutions for \(x\) are:

\[
x = \frac{-7 + \sqrt{65}}{4} \quad \text{or} \quad x = \frac{-7 - \sqrt{65}}{4}
\]

Do you want further explanation or help with the final decimal values?

Here are 5 related questions:
1. How does the discriminant affect the type of solutions?
2. Can you solve a quadratic equation by factoring when the discriminant is a perfect square?
3. What happens if the discriminant is negative?
4. How can you check your solutions to a quadratic equation?
5. How is the quadratic formula derived?

**Tip:** Always check the discriminant first to understand the nature of the roots (real, repeated, or complex).

Learn how to solve the quadratic equation 2x² + 7x - 2 = 0 using the quadratic formula. This step-by-step guide covers essential algebraic concepts for students in Grades 9-11, including the calculation of the discriminant and the application of the quadratic formula.

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