A general quintic equation a_5 x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0 = 0 can be reduced to one of the form y^5 + b_2 y^2 + b_1 y + b_0 = 0, called the principal quintic form.

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