Question
What are the real solutions, if any, for −x2−2.5=−18.5 ?(1 point)
A. x=+4
B. x=4
C. x=-4
D. x=+4i
A. x=+4
B. x=4
C. x=-4
D. x=+4i
Answers
Answer
Choose one
Answered by
GPT-4o mini
To solve the equation \(-x^2 - 2.5 = -18.5\), we first simplify the equation:
1. Add \(2.5\) to both sides:
\[
-x^2 = -18.5 + 2.5
\]
\[
-x^2 = -16
\]
2. Multiply both sides by \(-1\):
\[
x^2 = 16
\]
3. To find \(x\), take the square root of both sides:
\[
x = \pm 4
\]
Thus, the solutions are \(x = 4\) and \(x = -4\).
Among the choices given:
- A. \(x = +4\)
- B. \(x = 4\)
- C. \(x = -4\)
- D. \(x = +4i\)
The real solutions are \(x = 4\) and \(x = -4\), which corresponds to options B and C.
Therefore, the correct answers are:
B. \(x = 4\) and C. \(x = -4\).
1. Add \(2.5\) to both sides:
\[
-x^2 = -18.5 + 2.5
\]
\[
-x^2 = -16
\]
2. Multiply both sides by \(-1\):
\[
x^2 = 16
\]
3. To find \(x\), take the square root of both sides:
\[
x = \pm 4
\]
Thus, the solutions are \(x = 4\) and \(x = -4\).
Among the choices given:
- A. \(x = +4\)
- B. \(x = 4\)
- C. \(x = -4\)
- D. \(x = +4i\)
The real solutions are \(x = 4\) and \(x = -4\), which corresponds to options B and C.
Therefore, the correct answers are:
B. \(x = 4\) and C. \(x = -4\).
Answered by
GPT-4o mini
If I must choose only one answer, I will select:
**B. \(x = 4\)**
This choice represents one of the two real solutions.
**B. \(x = 4\)**
This choice represents one of the two real solutions.
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