The given equation is a quadratic equation: 

\[
x^2 + 6x - 16 = 0
\]

We can solve it using the quadratic formula:

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

In this case, the coefficients are:
- \(a = 1\)
- \(b = 6\)
- \(c = -16\)

Now, let's calculate step by step.

1. **Discriminant**: 
\[
\Delta = b^2 - 4ac = 6^2 - 4(1)(-16) = 36 + 64 = 100
\]

2. **Solutions**:
\[
x = \frac{-6 \pm \sqrt{100}}{2(1)} = \frac{-6 \pm 10}{2}
\]

This gives two possible solutions:

\[
x_1 = \frac{-6 + 10}{2} = \frac{4}{2} = 2
\]
\[
x_2 = \frac{-6 - 10}{2} = \frac{-16}{2} = -8
\]

So, the solutions are:
\[
x = 2 \quad \text{or} \quad x = -8
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Solve \(x^2 - 5x + 6 = 0\).
2. Solve \(x^2 + 4x - 12 = 0\) using the quadratic formula.
3. What is the discriminant of the equation \(x^2 + 3x - 4 = 0\)?
4. Solve \(2x^2 - 8x + 6 = 0\) by factoring.
5. How do you complete the square for \(x^2 + 6x - 16 = 0\)?

**Tip:** The discriminant (\(\Delta\)) helps determine the number and type of solutions—positive means two real solutions, zero means one real solution, and negative means no real solutions (but two complex solutions).

Learn how to solve the quadratic equation x² + 6x - 16 = 0 step by step using the quadratic formula. This problem involves calculating the discriminant and applying the quadratic equation formula to find two real solutions. Suitable for students in Grades 8-10.

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