Official Guide Explanation:
Problem Solving #172

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Solution and Metadata

Question: 172
Page: 176
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-One Unk >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: If (x - 1)² = 400, we can get closer to knowing the possible values of x by taking the square root of both sides: (x - 1) = 20 or (x - 1)= - 20. Since the question uses the words "could be," we're warned that there are multiple possible answers; in this case those come from the fact that x - 1 could be positive or negative 20. Solve each one, looking for x - 5 (what the question is asking for):

x - 1 = 20

x = 21

x - 5 = 21 - 5 = 16 (not an answer choice, so we have to keep looking)

x - 1= - 20

x= - 19

x - 5= - 19 - 5= - 24, choice (C).

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