what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 20?
Choose the correct answer: A) - 1 B) 6 C) 7 D) 12 E) 14
<gadget id="calculator">4 + 3</gadget>
<output>7</output>

<gadget id="calculator">3 - 4</gadget>
<output>-1</output>

<gadget id="calculator">7 + (-1)</gadget>
<output>6</output>

<result>B</result>
what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 20?
add(add(const_4, 3), subtract(3, const_4))
"first of all | x - 3 | ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + | x - 3 | = 20 . when x < 3 , x - 3 is negative , thus | x - 3 | = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 , x - 3 is non - negative , thus | x - 3 | = x - 3 . in this case we ' ll have ( x - 3 ) ^ 2 + ( x - 3 ) = 20 - - > x = - 2 or x = 7 . discard x = - 2 because it ' s not in the range we consider ( > = 3 ) . thus there are two solutions : x = - 1 and x = 7 - - > the sum = 6 . answer : b ."