Arrange, Then Root

x^2 - 49 = 0 is a difference of squares, and chapter five would factor it. But there is a faster read: move the 49 over, x^2 = 49, and un-square: x = ±7.

Both routes are legal and land on the same pair, as they must. Factoring gives (x + 7)(x - 7) = 0 and the split; the root method gives the ± in one move. For a bare x^2 = number, the root method is usually the shorter walk.

The arranging beat is the same one from the factoring chapter: isolate the squared thing first. Get x^2 alone on its side, and only then take roots.