The equation you provided appears to be:

\[
x^2 + \mod(x, 20) = 0
\]

where:

- \(x^2\) is \(x\) raised to the power of 2.
- \(\mod(x, 20)\) represents the remainder when \(x\) is divided by 20.

The equation can be broken down as:

\[
x^2 + \text{mod}(x, 20) = 0
\]

To solve this, follow these steps:

1. For each integer \(x\), calculate \(x^2\) (square of \(x\)).
2. Then calculate \(\mod(x, 20)\), the remainder when \(x\) is divided by 20.
3. Check when the sum of \(x^2\) and \(\mod(x, 20)\) equals 0.

Would you like me to compute specific solutions for this equation?

### Related questions:
1. What does the modulus operator mean in general math contexts?
2. Can we extend this method to moduli other than 20, like mod 30 or mod 10?
3. How do quadratic equations behave under different modulus operations?
4. What happens if we change the exponent to something other than 2, e.g., \(x^3 + \mod(x, 20) = 0\)?
5. What are common methods to solve equations involving both powers and mod operations?

### Tip:
When dealing with modulus operations in equations, always consider trying different values of \(x\) to find patterns or specific integer solutions.

Discover how to solve the equation x^2 + mod(x, 20) = 0, combining quadratic equations and modulus operations. Learn step-by-step methods to find integer solutions for this problem, suitable for Grades 9-12 math learners.

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