In the fiction of J. R. R. Tolkien, Edain is the term used by the Elves for Men who fought with them in the wars of Beleriand. Although Edain is the Elvish[?] word for all Men, it is usually applied only to those remained faithful to the Elves, and were given the island of Númenor as a reward.
... the square" is to add a constant (i.e., in this case, a quantity that does not depend on x) to the expression to the left of "=", that will make it a perfect square ...