We can solve the quadratic equation \( 9x^2 + 4x - 16 = 0 \) using the **quadratic formula**, which is:

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

For the equation \( 9x^2 + 4x - 16 = 0 \), the coefficients are:
- \( a = 9 \)
- \( b = 4 \)
- \( c = -16 \)

Now, substitute these values into the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{4^2 - 4(9)(-16)}}{2(9)}
\]

1. First, calculate the discriminant \( \Delta = b^2 - 4ac \):

\[
\Delta = 4^2 - 4(9)(-16) = 16 + 576 = 592
\]

2. Now, solve for \( x \):

\[
x = \frac{-4 \pm \sqrt{592}}{18}
\]

Since \( \sqrt{592} \approx 24.33 \), we have:

\[
x = \frac{-4 \pm 24.33}{18}
\]

Now, calculate the two possible solutions:

- \( x_1 = \frac{-4 + 24.33}{18} = \frac{20.33}{18} \approx 1.13 \)
- \( x_2 = \frac{-4 - 24.33}{18} = \frac{-28.33}{18} \approx -1.57 \)

So, the solutions are approximately:

\[
x_1 \approx 1.13 \quad \text{and} \quad x_2 \approx -1.57
\]

Would you like more details on any step?

Here are 5 related questions to explore:
1. How do you find the discriminant of a quadratic equation?
2. Why is the quadratic formula useful for solving any

Learn how to solve the quadratic equation 9x^2 + 4x - 16 = 0 step-by-step using the quadratic formula. This guide covers key concepts such as calculating the discriminant and applying the quadratic formula, perfect for students in Grades 9-10.

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