Who invented the principle of completing the square?

The Balylonians (around 400BC) first developed the algorithmic method for completing the square. But they didn't do it using equations, which they had no concept of, just a set of rules for particular cases. The Greeks, such as Euclid, showed geometrical proofs of the method. But it wasn't until the Persian mathematician al-Khawarizmi in the 9th century that the general algorithm was written down. Even this wasn't done using symbols like we use in algebra today but written out in prose.