Bot GPT 4-o mini To solve the equation \(-p^2 + 18 = 21\), we will first isolate \(p^2\).
-
Subtract 18 from both sides:
\[ -p^2 + 18 - 18 = 21 - 18 \]
This simplifies to:
\[ -p^2 = 3 \]
-
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 answer