https://file.aiquickdraw.com/mathbot/file/1728486431493293f35kk.jpg

The equation from the image is:

\[
x^2 + 8x - 50 = 0
\]

This is a quadratic equation, and we can solve it using the **quadratic formula**:

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

For the equation \(x^2 + 8x - 50 = 0\), we have the following coefficients:
- \(a = 1\)
- \(b = 8\)
- \(c = -50\)

### Step-by-step Solution:
1. **Calculate the discriminant**:
   \[
   \Delta = b^2 - 4ac = 8^2 - 4(1)(-50) = 64 + 200 = 264
   \]

2. **Apply the quadratic formula**:
   \[
   x = \frac{-8 \pm \sqrt{264}}{2(1)} = \frac{-8 \pm \sqrt{264}}{2}
   \]

3. **Simplify**:
   \(\sqrt{264}\) is approximately \(16.248\), so:
   \[
   x = \frac{-8 \pm 16.248}{2}
   \]

4. **Find the two solutions**:
   - First solution:
     \[
     x_1 = \frac{-8 + 16.248}{2} = \frac{8.248}{2} = 4.124
     \]
   - Second solution:
     \[
     x_2 = \frac{-8 - 16.248}{2} = \frac{-24.248}{2} = -12.124
     \]

### Final Solutions:
- \(x_1 \approx 4.124\)
- \(x_2 \approx -12.124\)

Would you like more details on any step, or do you have further questions?

Here are some related questions to consider:
1. How does the discriminant help us determine the number of solutions?
2. What is the significance of the quadratic formula?
3. Can this equation be factored easily instead of using the quadratic formula?
4. How can we graph the quadratic function to visualize its solutions?
5. What other methods can we use to solve quadratic equations?

**Tip:** When dealing with quadratic equations, always check if factoring is possible before applying the quadratic formula. It can sometimes lead to quicker results!

Solve the quadratic equation x^2 + 8x - 50 = 0

Learn how to solve the quadratic equation x^2 + 8x - 50 = 0 using the quadratic formula. The solution involves calculating the discriminant and applying the formula step-by-step. This is ideal for students in Grades 9-12 studying quadratic equations.

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