The method from rung 2 is right — the trouble is what people forget. A quadratic usually has two solutions, not one; and sometimes it has none. Both are about the sign on the right-hand side.
Trap One: Don't Drop the ±
Solving x² = 25, it's tempting to write just x = 5 and move on. But check the other one: (−5) × (−5) = 25 as well — a negative times a negative is positive. So x = −5 is also a real solution. Whenever the right side is a positive number, there are two answers, the + root and the − root. The toy shows both as dots either side of zero.
Trap Two: X² Can't Be Negative
Now try x² = −9. Square anything — positive or negative — and you get a positive (or zero). There is no real number you can square to get −9, so this equation has no real solution. It's not that the answer is hard; there genuinely isn't one. The toy throws these in on purpose so you learn to glance at the sign on the right before reaching for the root.
The Safety Check
Before you square-root, look at the right-hand side. Positive → two answers (mind the ±). Zero → one answer, x = 0. Negative → no real answer. That one glance kills both traps. And if you're ever unsure about a negative solution, square it and see — if it gives back k, it counts.