We are given the equation:

\[
36^2x + 25 = 0
\]

### Step 1: Simplify the term \(36^2\)
\[
36^2 = 36 \times 36 = 1296
\]
So the equation becomes:
\[
1296x + 25 = 0
\]

### Step 2: Isolate \(x\)
Subtract 25 from both sides:
\[
1296x = -25
\]

### Step 3: Solve for \(x\)
Divide both sides by 1296:
\[
x = \frac{-25}{1296}
\]

Thus, the solution is:
\[
x = -\frac{25}{1296}
\]

Would you like further details or have any questions? 

Here are five related questions to deepen your understanding:

1. What is the general approach for solving linear equations like this?
2. How do we interpret negative solutions in practical contexts?
3. Can you express \(\frac{-25}{1296}\) as a decimal?
4. How does changing the constant \(25\) affect the solution?
5. What would happen if the exponent in \(36^2\) was changed?

**Tip:** When solving linear equations, always isolate the variable by performing the opposite operation!

Learn how to solve the linear equation 36²x + 25 = 0 through detailed steps, including simplifying exponentiation and isolating the variable x. This problem is ideal for students in Grades 6-8 who want to deepen their understanding of algebraic concepts like simplification and solving equations.

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