Question

Which values are in the solution set of the quadratic equation, −9+(x−3)^2
_________
−4=−4
? Solve using square roots and choose all that apply.(2 points)
Responses

-8
-8

16
16

28
28

-22
-22

8
8

2
2

-2
-2

-10

Answer 1

what answers should I choose

Answer 2

To solve the equation \(-9 + (x-3)^2 - 4 = -4\), let's first simplify it.

Starting from the original equation:
\[
-9 + (x-3)^2 - 4 = -4
\]

This simplifies to:
\[
-13 + (x-3)^2 = -4
\]

Now, add 13 to both sides:
\[
(x-3)^2 = 9
\]

Next, we can take the square root of both sides:
\[
x-3 = 3 \quad \text{or} \quad x-3 = -3
\]

Now, solve for \(x\) in each case:
1. For \(x - 3 = 3\):
\[
x = 3 + 3 = 6
\]

2. For \(x - 3 = -3\):
\[
x = 3 - 3 = 0
\]

Thus, the values for \(x\) that solve the equation are \(6\) and \(0\).

None of the options provided in your list (-8, 16, 28, -22, 8, 2, -2, -10) are part of the solution set since the solutions we found are \(6\) and \(0\).

Answer 3

From the quadratic equation you provided, the solutions we found are \(x = 6\) and \(x = 0\). However, neither of these values is present in the list of response options you provided:

- -8
- 16
- 28
- -22
- 8
- 2
- -2
- -10

Since none of these options match the solutions \(6\) or \(0\), there are no correct answers to choose from the list you provided.

If you need to select from the provided options, please review the options or the original equation to ensure everything is correct.