Here’s the work:

Can you make sense of it? What’s the cause of this mistake? How could you help?

  • Outside of some sloppiness with the notation (and some sloppy handwriting) I see two mistakes as this student attempts to solve by completing the square. The first is when they replaced “-4” with “4”. I’m not exactly sure what was going on in their mind, but my guess would be that they either just dropped a sign or they were thinking about +/- when taking the square root of both sides of the equation. This led to a real answer instead of an imaginary one.

    The second mistake is when they take the root of both sides, they only take one possible answer (which they don’t write down) before they add two to both sides.