In about 300 BC Euclid developed a geometrical approach which, although later mathematicians used it to solve quadratic equations, amounted to finding a length which in our notation was the root of a quadratic equation. However all Babylonian problems had answers which were positive (more accurately unsigned ) quantities since the usual answer was a length. The method is essentially one of completing the square. What they did develop was an algorithmic approach to solving problems which, in our terminology, would give rise to a quadratic equation. This is an over simplification, for the Babylonians had no notion of 'equation'.
It is often claimed that the Babylonians (about 400 BC ) were the first to solve quadratic equations.
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