https://file.aiquickdraw.com/mathbot/file/1725483921428xrzpyto8.jpg

The equation provided in the image is:

\[
x^2 + 5x - 14 = 0
\]

To solve this quadratic equation, we can use the quadratic formula:

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

For the given equation \( ax^2 + bx + c = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = 5 \)
- \( c = -14 \)

Now, let's calculate the discriminant and solve for \( x \):

\[
\text{Discriminant} = b^2 - 4ac = 5^2 - 4(1)(-14)
\]

\[
\text{Discriminant} = 25 + 56 = 81
\]

Since the discriminant is a perfect square, the roots are real and distinct:

\[
x = \frac{-5 \pm \sqrt{81}}{2 \times 1} = \frac{-5 \pm 9}{2}
\]

This gives us two solutions:

\[
x_1 = \frac{-5 + 9}{2} = \frac{4}{2} = 2
\]

\[
x_2 = \frac{-5 - 9}{2} = \frac{-14}{2} = -7
\]

Therefore, the solutions are \( x = 2 \) and \( x = -7 \).

Would you like more details on the solution, or do you have any questions? 

Here are five related questions that you might find interesting:
1. How does the discriminant help determine the nature of the roots in a quadratic equation?
2. What are the possible scenarios for the discriminant (positive, zero, negative), and how do they affect the roots?
3. Can all quadratic equations be solved by factoring, and why might the quadratic formula be necessary?
4. How can you use completing the square to solve a quadratic equation?
5. What real-world problems can be modeled by quadratic equations?

**Tip:** Always check the discriminant first when solving a quadratic equation, as it provides useful information about the roots before solving.

Solve the quadratic equation x^2 + 5x - 14 = 0

Learn how to solve the quadratic equation x^2 + 5x - 14 = 0 using the quadratic formula. This detailed solution covers key algebraic concepts, including discriminant calculation and determining the nature of the roots. Suitable for students in Grades 8-10.

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