Question

Use the quadratic formula to solve x² + 8x + 9 = 0.

What are the solutions to the equation?

Round irrational solutions to the nearest tenth.



Responses

x=−1.2 and x=−6.8
x equals negative 1.2 and x equals negative 6.8

x = 1 and x=−9
x = 1 and x equals negative 9

x=−1 and x=−8
x equals negative 1 and x equals negative 8

x=−6.6 and x=−1.4

Answer 1

To solve the equation \( x^2 + 8x + 9 = 0 \) using the quadratic formula, we first identify \( a \), \( b \), and \( c \) from the standard form \( ax^2 + bx + c = 0 \):

- \( a = 1 \)
- \( b = 8 \)
- \( c = 9 \)

The quadratic formula is given by:

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

Next, we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = 8^2 - 4 \cdot 1 \cdot 9 = 64 - 36 = 28
\]

Now we substitute the values into the quadratic formula:

\[
x = \frac{-8 \pm \sqrt{28}}{2 \cdot 1}
\]

We simplify \( \sqrt{28} \):

\[
\sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7}
\]

Substituting this back into the equation gives:

\[
x = \frac{-8 \pm 2\sqrt{7}}{2}
\]

We can simplify this further:

\[
x = -4 \pm \sqrt{7}
\]

Now we approximate \( \sqrt{7} \):

\[
\sqrt{7} \approx 2.64575
\]

Thus, we have the two solutions:

\[
x_1 = -4 + \sqrt{7} \approx -4 + 2.64575 \approx -1.35425 \quad \text{(rounded to -1.4)}
\]
\[
x_2 = -4 - \sqrt{7} \approx -4 - 2.64575 \approx -6.64575 \quad \text{(rounded to -6.6)}
\]

So, the solutions to the equation are approximately:

\[
x \approx -1.4 \text{ and } x \approx -6.6
\]

From your response options, the correct answer is:

**x = -6.6 and x = -1.4**.