What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 ?  Options:
A) -1
B) 6
C) 7
D) 12
E) 14
First of all |x - 3|^2 = (x - 3)^2, so we have: (x - 3)^2 + |x - 3| = 20.   When x &lt; 3, x - 3 is negative, thus |x - 3| = -(x - 3). In this case we'll have (x - 3)^2 - (x - 3) = 20 --&gt; x = -1 or x = 8. Discard x = 8 because it's not in the range we consider (&lt; 3).   When x &gt;= 3, x - 3 is non-negative, thus |x - 3| = x - 3. In this case we'll have (x - 3)^2 + (x - 3) = 20 --&gt; x = -2 or x = 7. Discard x = -2 because it's not in the range we consider (&gt;= 3).   Thus there are two solutions: x = -1 and x = 7 --&gt; the sum = 6.   Answer: 6.
<result>B</result>
What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 ?