find the negative solution of 0 = x^2 +16x - 17

To find the negative solution of the quadratic equation \(0 = x^2 + 16x - 17\), we can use the quadratic formula:

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

For the equation \(x^2 + 16x - 17 = 0\):

- \(a = 1\)
- \(b = 16\)
- \(c = -17\)

Now, plug these values into the quadratic formula:

\[
x = \frac{-16 \pm \sqrt{16^2 - 4(1)(-17)}}{2(1)}
\]

\[
x = \frac{-16 \pm \sqrt{256 + 68}}{2}
\]

\[
x = \frac{-16 \pm \sqrt{324}}{2}
\]

\[
x = \frac{-16 \pm 18}{2}
\]

Now, compute the two possible values of \(x\):

1. \(x = \frac{-16 + 18}{2} = \frac{2}{2} = 1\)
2. \(x = \frac{-16 - 18}{2} = \frac{-34}{2} = -17\)

The negative solution is \(x = -17\).

Would you like more details or have any questions? Here are some related questions:

1. How do you derive the quadratic formula?
2. What are the steps for completing the square in a quadratic equation?
3. How can you determine the nature of the roots of a quadratic equation?
4. What is the discriminant, and how is it used in quadratic equations?
5. How can you solve quadratic equations by factoring?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) before solving a quadratic equation to determine if the roots are real or complex.

Discover how to find the negative solution of the quadratic equation x^2 + 16x - 17 = 0 using the quadratic formula. Follow a detailed step-by-step solution with clear explanations and calculations. Suitable for high school students studying quadratic equations.

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