We are given the equation:

\[
P^2 - p = 4
\]

To solve for \( P \) in terms of \( p \), we can proceed step by step:

### Step 1: Rearrange the equation to isolate \( P^2 \)
\[
P^2 = 4 + p
\]

### Step 2: Solve for \( P \)
Take the square root of both sides:
\[
P = \pm \sqrt{4 + p}
\]

Thus, the solution is:

\[
P = \pm \sqrt{4 + p}
\]

Would you like more details or clarifications on any part of the process?

Here are some related questions:
1. How do we solve similar equations involving squares?
2. What if we are given specific values for \( p \)?
3. Can this equation be solved graphically?
4. What happens if \( 4 + p \) is negative?
5. How do square roots affect the solutions?

**Tip**: When taking the square root of a number, remember to account for both the positive and negative roots!

Explore how to solve the equation P^2 - p = 4 by isolating P and taking square roots. This solution demonstrates algebraic techniques suitable for students in Grades 9-12, involving square root properties and equation rearrangement.

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