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The given inequality is:

\[
-x^2 - 25 \leq 0
\]

### Step-by-step solution:

1. First, simplify the inequality:
\[
-x^2 - 25 \leq 0
\]
Add \(25\) to both sides:
\[
-x^2 \leq 25
\]

2. Next, divide by \(-1\) to solve for \(x^2\). Remember, dividing by a negative number reverses the inequality:
\[
x^2 \geq -25
\]

3. Since \(x^2\) is always non-negative (i.e., \(x^2 \geq 0\) for all real values of \(x\)), this inequality is always true, because \(x^2 \geq -25\) holds for any real number \(x\). There is no restriction on the values of \(x\).

Thus, the solution to this inequality is all real numbers.

### Graph of the solution:
Since the inequality holds for all real numbers, the graph will be a number line where all values from \(-\infty\) to \(+\infty\) are included.

- The correct option is **C**, which shows all real numbers included in the solution.

Do you want further clarification or more details?

### Related questions:
1. What would the solution be if the inequality was \(x^2 \leq 25\)?
2. How does squaring affect the direction of inequalities?
3. Can the inequality \(x^2 \geq -25\) ever be false?
4. How does the graph change if the inequality was strict (i.e., \(-x^2 - 25 < 0\))?
5. What is the significance of \(x^2 \geq 0\) in this context?

### Tip:
Always remember that squaring a real number results in a non-negative value, which simplifies solving inequalities involving squares.

Solve the given inequality -x^2 - 25 ≤ 0 and choose the graph of its solution.

Learn how to solve the quadratic inequality -x^2 - 25 ≤ 0. The problem explores key concepts in algebra and inequality solving, showing that the solution is all real numbers. Suitable for students in Grades 9-11.

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