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 $i$.