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The given equation is:

\[
553 = \sqrt{(471498 - x)^2 + (611738 - y)^2}
\]

This equation represents the distance between the point \((x, y)\) and the fixed point \((471498, 611738)\), which equals 553.

To solve for \(x\) and \(y\), we can first eliminate the square root by squaring both sides of the equation:

\[
553^2 = (471498 - x)^2 + (611738 - y)^2
\]

Let me perform the necessary steps to simplify the equation.After squaring both sides of the equation, we get:

\[
305809 = (471498 - x)^2 + (611738 - y)^2
\]

This equation represents a circle with a radius of 553 units and a center at \((471498, 611738)\). However, to solve for \(x\) and \(y\), we need more information or constraints (such as one of the variables being given or additional equations).

Would you like to provide more details or context to proceed? Let me know if you'd like further clarification on this, or if you want me to expand the explanation.

### Related Questions:
1. How do you determine the equation of a circle from a geometric context?
2. What methods are used to solve systems of nonlinear equations?
3. Can you explain how to find points on a circle given its equation?
4. What are some practical applications of distance formulas in geometry?
5. How do we derive the general form of a circle's equation?

### Tip:
Always check the number of unknowns and equations before trying to solve. If there are more unknowns than equations, more information is required.

Solve for x and y in the equation: 553 = √((471498 - x)² + (611738 - y)²)

Learn how to solve for the coordinates x and y in the equation 553 = √((471498 - x)² + (611738 - y)²), representing a point on a circle with a center at (471498, 611738) and a radius of 553 units. Explore key geometry concepts including the distance formula and the equation of a circle.

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