| { | |
| "problem": "If $(x+2)(x-3)=14$, find the sum of the possible values of $x$.", | |
| "level": "Level 3", | |
| "type": "Algebra", | |
| "solution": "Expanding the left side of the given equation, we have $x^2-x-6=14 \\Rightarrow x^2-x-20=0$. Since in a quadratic with equation of the form $ax^2+bx+c=0$ the sum of the roots is $-b/a$, the sum of the roots of the given equation is $1/1=\\boxed{1}$." | |
| } |