The equation x² + 10x + 21 = 0 has solutions x=-3 and x=-7. What is the sum of the solutions?

The sum of the solutions is $-3+(-7)=-10$, choice G. This matches the rule for $x^2+bx+c=0$ that the sum of the roots is $-b$, here $-10$, and the product of the roots is $c$, here $(-3)(-7)=21$. Choice F ($-21$) is the constant term, not the sum. Choice J ($10$) is the opposite of the sum, which comes from forgetting the signs of the roots. Choice H ($4$) is the difference of the roots, $-3-(-7)$. The question asks for the sum, so no further solving is necessary.