PSAT Math Multiple-Choice Question 437: Answer and Explanation

Question: 437

Which of the following is equivalent to x² - 6x + 10 = 0?

• A. (x - 3)² = -1
• B. (x + 3)² = 1
• C. (x - 6)² = -26
• D. (x + 6)² = 26

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Completing the Square

Getting to the Answer: The format of the answer choices makes completing the square the best approach for this question. Since the first term has a constant of 1, that makes completing the square more straightforward. Make sure to move the constant term to the right side of the equation before dividing the x term constant by 2 and squaring. Also, make sure that the squared term contains a negative constant since the x term in the original quadratic is negative:

Therefore, (A) is correct. Note that (C) is the result if you forgot to divide b by 2.