https://file.aiquickdraw.com/mathbot/file/17241873471620g50hyx4.jpg

The equation shown in the image is:

\[
2x^2 + 15x + 7 = 0
\]

This is a quadratic equation. To solve it, we can use the **quadratic formula**, which is:

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

For the given equation \(2x^2 + 15x + 7 = 0\), the coefficients are:

- \(a = 2\)
- \(b = 15\)
- \(c = 7\)

Let's plug these values into the quadratic formula:

\[
x = \frac{-15 \pm \sqrt{15^2 - 4(2)(7)}}{2(2)}
\]

Now, let's calculate the discriminant and then find the roots.The solutions to the quadratic equation \(2x^2 + 15x + 7 = 0\) are:

\[
x_1 = -0.5 \quad \text{and} \quad x_2 = -7.0
\]

These are the roots of the equation.

Would you like more details on how this solution was derived, or do you have any other questions?

Here are five related questions for further exploration:

1. How does the discriminant in the quadratic formula determine the nature of the roots?
2. What is the significance of the roots in the context of a quadratic function's graph?
3. Can quadratic equations always be solved using factoring, or are there cases where the quadratic formula is necessary?
4. How do the roots of the equation relate to the vertex of the parabola?
5. What happens if the discriminant is negative?

**Tip:** The quadratic formula is a powerful tool that works for any quadratic equation, even when the roots are complex (involving imaginary numbers).

Learn how to solve the quadratic equation 2x^2 + 15x + 7 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula and solving quadratic equations. Suitable for high school students.

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