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Theorem: The equation has two solutions when and they are . A unique solution for . And non-real solutions for which are .
Proof: Check that for those solutions satisfy the equation. Furthermore because the complex numbers are a field (a type of algebra) there is at most 2 solutions. Thus those need to be it. If then, since it has no zero divisor (no non-zero numbers that give zero) we conclude that is the only solution.
(NOTE: No negative square roots were used).