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The answer to the question depends on the set of numbers within which you are working.

If you are working in integers, x2 = 2.25 has no solution. However, it does have a solution in rational numbers (x = 1.5).

If working with rationals, x2 = 6 has no rational solution but it does have a solution in real numbers.

Yet again, x2 = -6 has no solution in the reals, but does have a solution in complex numbers.

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