Luca solved an equation as shown, and verified that his solution was correct.Explain what Luca’s error is and why his answer is not completely correct.

Answer:

Luca incorrectly squares the right side: (√(x − 3) + 1)² includes the cross term 2√(x − 3), which he omitted. This causes him to miss the other solution, x = 7. Both x = 3 and x = 7 satisfy the original equation, so his answer is not complete.