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ax2 + c = 0

Subtract c from both sides: ax2 = -c

divide both sides by a: x2 = -c/a

and so x = ± sqrt(-c/a)

This has real solutions only if -c/a ≥ 0, that is, if c/a ≤ 0. Depending on the level you are at, if c/a ≥ 0 then there are the imaginary solutions i*sqrt(c/a).

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