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
16
16
8
8
-2
-2
-8
-8
2
2
28
28
-10
-10
-22
-22
? Solve using square roots and choose all that apply.(2 points)
Responses
16
16
8
8
-2
-2
-8
-8
2
2
28
28
-10
-10
-22
-22
Answers
Answer
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
16
16
8
8
-2
-2
-8
-8
2
2
28
28
-10
-10
-22
-22
try again
? Solve using square roots and choose all that apply.(2 points)
Responses
16
16
8
8
-2
-2
-8
-8
2
2
28
28
-10
-10
-22
-22
try again
Answered by
GPT-4o mini
To solve the quadratic equation \(-9 + \frac{(x-3)^2}{-4} = -4\), we'll first rearrange the equation to isolate the square term.
1. Start by adding 9 to both sides:
\[
\frac{(x-3)^2}{-4} = -4 + 9
\]
\[
\frac{(x-3)^2}{-4} = 5
\]
2. Multiply both sides by -4:
\[
(x-3)^2 = -20
\]
At this point, we see that \((x-3)^2 = -20\). A square cannot equal a negative number in the set of real numbers. This means that there are no real solutions to this equation. As such, none of the provided values (16, 8, -2, -8, 2, 28, -10, -22) are in the solution set since the solution set is empty.
Thus, the answer is that there are no valid responses to select from the provided options.
1. Start by adding 9 to both sides:
\[
\frac{(x-3)^2}{-4} = -4 + 9
\]
\[
\frac{(x-3)^2}{-4} = 5
\]
2. Multiply both sides by -4:
\[
(x-3)^2 = -20
\]
At this point, we see that \((x-3)^2 = -20\). A square cannot equal a negative number in the set of real numbers. This means that there are no real solutions to this equation. As such, none of the provided values (16, 8, -2, -8, 2, 28, -10, -22) are in the solution set since the solution set is empty.
Thus, the answer is that there are no valid responses to select from the provided options.
Answered by
GPT-4o mini
Let’s solve the quadratic equation step-by-step again for clarity. The equation given is:
\[
-9 + \frac{(x - 3)^2}{-4} = -4
\]
### Step 1: Isolate the square term
1. First, add 9 to both sides of the equation:
\[
\frac{(x - 3)^2}{-4} = -4 + 9
\]
\[
\frac{(x - 3)^2}{-4} = 5
\]
### Step 2: Eliminate the fraction
2. Next, multiply both sides by -4 to eliminate the fraction:
\[
(x - 3)^2 = -20
\]
### Step 3: Analyze the equation
At this point, \((x - 3)^2 = -20\).
Since the square of a real number cannot equal a negative number, there are no real solutions to this equation. Therefore, the equation has no valid solutions.
### Conclusion
The solution set is empty, meaning none of the provided values (16, 8, -2, -8, 2, 28, -10, -22) are solutions to the equation.
Thus, **there are no values from the options that are in the solution set**.
\[
-9 + \frac{(x - 3)^2}{-4} = -4
\]
### Step 1: Isolate the square term
1. First, add 9 to both sides of the equation:
\[
\frac{(x - 3)^2}{-4} = -4 + 9
\]
\[
\frac{(x - 3)^2}{-4} = 5
\]
### Step 2: Eliminate the fraction
2. Next, multiply both sides by -4 to eliminate the fraction:
\[
(x - 3)^2 = -20
\]
### Step 3: Analyze the equation
At this point, \((x - 3)^2 = -20\).
Since the square of a real number cannot equal a negative number, there are no real solutions to this equation. Therefore, the equation has no valid solutions.
### Conclusion
The solution set is empty, meaning none of the provided values (16, 8, -2, -8, 2, 28, -10, -22) are solutions to the equation.
Thus, **there are no values from the options that are in the solution set**.
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