Question
What value of p is a solution to this equation?
–
p
2
+18=21
–
p
2
+18=21
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \(-p^2 + 18 = 21\), we will first isolate \(p^2\).
1. Subtract 18 from both sides:
\[
-p^2 + 18 - 18 = 21 - 18
\]
This simplifies to:
\[
-p^2 = 3
\]
2. Now, multiply both sides by -1:
\[
p^2 = -3
\]
Since \(p^2\) cannot be negative in the set of real numbers, this equation has no real solutions. If we consider complex numbers, we can take the square root:
\[
p = \pm \sqrt{-3} = \pm i\sqrt{3}
\]
So the solutions in the complex number system are:
\[
p = i\sqrt{3} \quad \text{and} \quad p = -i\sqrt{3}
\]
1. Subtract 18 from both sides:
\[
-p^2 + 18 - 18 = 21 - 18
\]
This simplifies to:
\[
-p^2 = 3
\]
2. Now, multiply both sides by -1:
\[
p^2 = -3
\]
Since \(p^2\) cannot be negative in the set of real numbers, this equation has no real solutions. If we consider complex numbers, we can take the square root:
\[
p = \pm \sqrt{-3} = \pm i\sqrt{3}
\]
So the solutions in the complex number system are:
\[
p = i\sqrt{3} \quad \text{and} \quad p = -i\sqrt{3}
\]
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