The expression you provided is a quadratic equation:

\[
2x^2 + 17x + 21
\]

Would you like to solve this quadratic equation, factor it, or analyze its features (such as finding the vertex, roots, etc.)? I will proceed with solving it unless you specify otherwise.

### Solving the quadratic equation:
We can use the quadratic formula:

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

For the equation \(2x^2 + 17x + 21\), the coefficients are:
- \(a = 2\)
- \(b = 17\)
- \(c = 21\)

Now, let's calculate the discriminant (\(\Delta\)):

\[
\Delta = b^2 - 4ac = 17^2 - 4(2)(21) = 289 - 168 = 121
\]

Since the discriminant is a perfect square, we will have two real, rational roots.

Now, substitute these values into the quadratic formula:

\[
x = \frac{-17 \pm \sqrt{121}}{2(2)} = \frac{-17 \pm 11}{4}
\]

Now, calculate both possible solutions:

\[
x_1 = \frac{-17 + 11}{4} = \frac{-6}{4} = -\frac{3}{2}
\]
\[
x_2 = \frac{-17 - 11}{4} = \frac{-28}{4} = -7
\]

### The solutions are:
\[
x_1 = -\frac{3}{2}, \quad x_2 = -7
\]

Let me know if you'd like further details or a different approach!

---

Here are 5 related questions to deepen understanding:
1. How can you factor the quadratic equation \(2x^2 + 17x + 21\)?
2. What is the vertex of the parabola represented by \(2x^2 + 17x + 21\)?
3. How does the discriminant (\(\Delta\)) help determine the nature of the roots?
4. Can you rewrite this quadratic equation in vertex form?
5. What are the axis of symmetry and the maximum/minimum values for the function \(y = 2x^2 + 17x + 21\)?

**Tip:** Always check the discriminant first to determine if solving by factoring is possible!

This page provides a step-by-step solution to the quadratic equation 2x^2 + 17x + 21. Learn how to use the quadratic formula to find the roots, calculate the discriminant, and understand the nature of the solutions. Perfect for students in Grades 9-10.

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