Question

Use the quadratic formula to solve the following quadratic equation:

x2+2x−8=0
(1 point)
Responses

x=10, x=−8
x=10, x=−8

x=−10, x=8
x=−10, x=8

x=−2, x=4
x=−2, x=4

x=2, x=−4

Answer 1

To solve the quadratic equation \( x^2 + 2x - 8 = 0 \) using the quadratic formula, we start by identifying the coefficients \( a \), \( b \), and \( c \):

- \( a = 1 \)
- \( b = 2 \)
- \( c = -8 \)

The quadratic formula is given by:

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

Now, let's calculate:

1. Calculate \( b^2 - 4ac \):

\[
b^2 = 2^2 = 4
\]
\[
4ac = 4(1)(-8) = -32
\]
\[
b^2 - 4ac = 4 - (-32) = 4 + 32 = 36
\]

2. Now substitute into the quadratic formula:

\[
x = \frac{{-2 \pm \sqrt{36}}}{2 \cdot 1}
\]
\[
x = \frac{{-2 \pm 6}}{2}
\]

3. This gives us two solutions:

- For the positive root:

\[
x = \frac{{-2 + 6}}{2} = \frac{4}{2} = 2
\]

- For the negative root:

\[
x = \frac{{-2 - 6}}{2} = \frac{-8}{2} = -4
\]

So, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are:

\[
x = 2 \quad \text{and} \quad x = -4
\]

Therefore, the correct response is:

**x=2, x=−4**