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Q&A #18119 |
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Just a little addendum on the history of this method (I was writing up a article on this and thought of your question). The substitution of Z=ax to make a solution pliable dates back to the ancient Babylonian clay tablets according to Boyer's History of Mathematics. They used it in order to make a trinomial (ax)^2 + b(ax) =ac so that they could solve using their method of completing the square. The idea of factoring had to wait a LONG time until Thomas Harriot came up with it around 1600-1621 (he died in 1621 but his method was not published until 1631, ten years after his death).. By the way, I can not find any reference to "bottoms up" name for this... can you help ME? -Pat Ballew, for the T2T service
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