What is the sum of all possible solutions to |x - 4|^2 + |x - 4| = 12 ?
Answers.
A) 3  B) 4  C) 5  D) 6  E) 7
Denote |x - 4| as y: y^2 + y = 12 --&gt; y = -4 or y = 3. Discard the first solution since y = |x - 4|, so it's an absolute value and thus cannot be negative.   y = |x - 4| = 3 --&gt; x = 7 or x = 0. The sum = 7.   Answer: 7.
<result>E</result>
What is the sum of all possible solutions to |x - 4|^2 + |x - 4| = 12 ?