Two variables... One equation?

Algebra Level 3

If \((x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}), ..., (x_{n}, y_{n})\) are the real co-ordinates which are the solution(s) to the equation

\((4x^{2} - 12x + 25)(y^{2} - 4y + 8) = 64\),

Find \( (\sum _{i = 1}^{n}x_{i} + y_{i}) - 0.5\)

This is a modified AITMO 2013 problem.

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