As Mrs. Broderick was creating this test she solved the following equation by completing the square.
\[
3 x^{2}-18 x-6=0
\]
Step \( 13 x^{2}-18 x=6 \)
Step \( 2 \quad x^{2}-6 x=2 \)
Step \( 3 \quad x^{2}-6 x+3=6 \)
Step \( 4 \quad(x-3)^{2}=6 \)
Step \( 5 x-3= \pm \sqrt{6} \)
Step \( 6 \quad x=3 \pm \sqrt{6} \)
On which step, if any, did she make a mistake?
Step 2, she forgot to divide all terms by the leading coefficient.
Step 4, she factored incorrectly.
No mistake was made. Mrs. Broderick never makes mistakes.
Step 5, she forgot to simplify the square root.
Step 3, she forgot to square half of the middle term before adding it to both sides.
