Digital PSAT Math Practice Question 281: Answer and Explanation

Question: 281

x² - 20 = x

What are the solution(s) to the equation above?

• A. 20
• B. 12, 5
• C. -4, 5
• D. 0, 2

Correct Answer: C

Explanation:

(C) Subtract x from both sides to give the quadratic

x² - x - 20 = 0.

This quadratic easily factors to

(x - 5)(x + 4) = 0

If either factor equaled 0, the entire expression would equal to 0. Thus, you can find the two solutions to the equation by setting each factor to 0:

x - 5 = 0, so x = 5.

x + 4 = 0, so x = - 4.

Therefore, the two solutions are - 4 and 5.

Alternatively, if you aren't great at factoring, you could have used the quadratic formula to arrive at the same answer.

If you have no idea how to solve this problem, you could plug each answer choice into the equation to see which numbers actually work. For instance, you can eliminate choice (A) because 20² - 20 = 400 - 20 = 380 ≠ 20.