PSAT Math Multiple-Choice Question 472: Answer and Explanation

Question: 472

Which of the following is a solution to the equation x² + 24 = 14x - x² ?

• A. -3
• B.
• C. 4
• D. 7

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Solving Quadratics by Factoring

Getting to the Answer: Rearrange the equation into the standard quadratic form by subtracting everything from the right side of the equal sign: . Next, divide the equation by 2 to make factoring easier: . Now, use reverse FOIL to determine the factors. You need factors of 12 that sum to -7. Those are -3 and -4, so your equation factors to (x - 3)(x - 4) = 0. That means the solutions to the equation are x = 3 and x = 4. Since only one of these is among the answers, (C) is correct.