The student’s work is not correct. Here’s what went wrong:
In the solution #2 step, the student incorrectly set up the equation to find the second solution. Instead of solving \( x + 9 = 0 \), the student should have used \( x - 9 = 0 \).
The correct steps should be:
- From \( (x - 2)(x - 9) = 0 \), set each factor equal to zero:
- \( x - 2 = 0 \) leads to \( x = 2 \) (this solution is correct)
- \( x - 9 = 0 \) leads to \( x = 9 \) (this solution was missed)
Therefore, the correct conclusion is: No, there should be a solution #3.