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The task requires you to arrange the expressions in the correct order to check the solution for \(-25\), likely relating to complex numbers or square roots. Let's break this down step by step:

### Key Ideas:
- \(i\) is the imaginary unit where \(i^2 = -1\).
- The square root of a negative number involves imaginary numbers. For example, \(\sqrt{-25} = 5i\), because \((5i)^2 = -25\).

### Possible Steps in the Solution:
1. **Start with the given number**:
   \(-25 = \)
   - You’ll need the expression that represents this (perhaps as \((25)(-1)\)).

2. **Convert it using imaginary numbers**:
   \(-25\) can be written as \( (5i)^2 \) because \( (5i)^2 = 25 \times (-1) = -25 \).
   
3. **Represent using squared terms**:
   The next step would be something like \( (5i)^2 = -25 \).

4. **Check with intermediate values**:
   You might need to confirm that \(5i\) is a root of \(-25\).

5. **Final equality check**:
   \( -25 = -25 \) to confirm the solution.

### Matching with Options:
Here are the corresponding values in the drag-and-drop area:
1. **\((25)(-1)\)** to represent \(-25\).
2. **\((\pm 5i)^2\)** to show the square of \(5i\).
3. **\(-25\)** as the final result of \((5i)^2\).
4. **25** and **\(-1\)** as intermediary steps.

Try arranging:
1. \(-25 = (25)(-1)\),
2. \( (25)(-1) = (\pm 5i)^2\),
3. \( (\pm 5i)^2 = -25 \).

Would you like more details or clarification on this? Let me know!

Here are 5 related questions:
1. How do imaginary numbers simplify square roots of negative values?
2. What is the significance of \(i\) in complex number theory?
3. Can all negative numbers be expressed as squares of imaginary numbers?
4. How would the steps change if the number were different (e.g., \(-16\))?
5. How does the rule \(i^2 = -1\) impact operations in the complex plane?

**Tip**: When dealing with imaginary numbers, always simplify square roots by factoring negative signs into \(i\).

Find the check steps for the solutions in the correct order for the equation involving -25.

Learn how to check the solution for the equation involving -25, which involves complex numbers and the imaginary unit i. The step-by-step process includes using properties of imaginary numbers and understanding how to represent negative values as squares of complex numbers.

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