I see how to derive the quadratic formula, but I have what I believeis a historical question: I've read about how Babylonianmathematicians used the method of completing the square to solvequadratic equations with positive roots, but did not have a generalformula, and having the formula would have helped them. But what were they trying to do in the first place, that left themwith quadratic equations in their laps to begin with? Measuring land area?
The same with cubic equations that the Greeks, Arabs, and Chinese weretrying to solve centuries later. What was the physical problem thatplopped these equations into their laps to begin with?