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!

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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!