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Why is the Quintic Unsolvable?
In this article, I hope to convince you that the quintic equation is unsolvable, in the sense that I can’t write down the solution to the equation \[ ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0 \] using only addition, subtraction, multiplication, division, raising to an integer power, and taking an integer root. In fact, I…