Advanced Math practice question

Answer: B. b = −4

Complete the square: x² + 6x + 5 = (x² + 6x + 9) − 9 + 5 = (x + 3)² − 4, so a = 3 and b = −4. The trap is choice A, leaving b as the original constant 5 without accounting for the −9 added to complete the square.

Why the other answers are wrong

A. b = 5

You kept the original constant 5 as b, but completing the square adds 9 inside the parentheses, so you must subtract 9: 5 − 9 = −4.

C. b = 9

9 is the number you add to make x² + 6x a perfect square, not the leftover constant. After writing (x + 3)², subtract that 9 back out: 5 − 9 = −4.

D. b = 14

You added 9 to the constant instead of subtracting it: 5 + 9 = 14. Since you inserted 9 to build (x + 3)², it has to come back off, giving 5 − 9 = −4.

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