Question

Question
Solve for x
.
−x4−2=−10
(1 point)
Responses

x=−2
x equals negative 2

x=3
x equals 3

x=32
x equals 32

x=48

Answer 1

To solve for \( x \) in the equation:

\[
-x^4 - 2 = -10
\]

First, we can rearrange the equation to isolate \( -x^4 \):

\[
-x^4 = -10 + 2
\]

This simplifies to:

\[
-x^4 = -8
\]

Now, multiplying both sides by -1 gives:

\[
x^4 = 8
\]

Next, we take the fourth root of both sides:

\[
x = \pm \sqrt[4]{8}
\]

Since \( \sqrt[4]{8} = \sqrt{2^3} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \), we can express our solutions as:

\[
x = \pm 2\sqrt{2}
\]

Now, let's evaluate the given options:

1. \( x = -2 \)
2. \( x = 3 \)
3. \( x = 32 \)
4. \( x = 48 \)

None of these options are correct because neither \( 2\sqrt{2} \) nor \( -2\sqrt{2} \) corresponds to the options given. However, if we approximate \( 2\sqrt{2} \):

- \( \sqrt{2} \approx 1.414 \)
- Thus, \( 2\sqrt{2} \approx 2.828 \)

Given the approximations, none of the original answer choices provided correspond to the correct solution.

Thus, the answer is that none of the provided options are correct based on the solution derived.