Undoing a Square

Some quadratics have no middle term at all: x^2 = 25. No pair to hunt; the x is only squared. Undo the square directly: take the square root of both sides.

But carefully: TWO numbers square to 25, namely 5 and -5. Undoing a square therefore splits into two cases, x = 5 or x = -5, usually written x = ±5 in one breath.

Forgetting the negative root is this chapter's classic error. The square wiped out the sign, so the un-squaring must offer both signs back. On the board, tap the squared side: the move writes both cases for you to finish.