What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 30 ? Choose the correct choice.
A) 4
B) 5
C) 3
D) 2
E) 1
Denote |x - 3| as y: y^2 + y = 30 --&gt; y = -6 or y = 5. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.   y = |x - 3| = 5 --&gt; x = 8 or x = -3. The sum = 5.   Answer: 5.
<result>B</result>
What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 30 ?