Explanation for Question 8 From the Math (No Calc) Section on the 2020 October Sat
So question number eight is asking us for the, some of the solutions with 2 an S to the given equation. 3 And we noticed that this is the equation of a quadratic formula, 4 right? It could be a parabola and we know this because it has an 5 X squared and an X. And so whenever you see this, 6 this is a cause to know that you can factor this equation and then 7 you can get two or more solutions. 8 And so here, we just want to factor this equation. If we remember factoring, 9 we know that the number at the end, we want to multiply to get 10 this number. And then in the num the number in the middle, 11 we want to add to get this number. So we need two numbers that 12 multiply to get as positive 35, and add to get us a negative 12. 13 We can see that that's going to be five and seven will give us 14 35, but if we want to get the negative 12 to add together, 15 we need negative five and negative seven. 16 So this is really simple. So this is just an X squared. 17 We just put an X in front of both, both sets of parentheses. 18 And then one of our numbers was negative five. 19 So we just put in a negative five. The other number was a negative 20 seven. So we just put in a negative seven. And now this isn't the 21 solution, right? To find the solution. We have to take each set of parentheses 22 and set it equal to zero. When I do this, 23 I can add five to both sides and I can get the X is 24 equal to five for this other one. 25 I can add seven to both sides and I can get X is equal 26 to seven. So at this point I've solved for both of my solutions and 27 I'm almost done. All I have to do is find the sum. 28 I just have to add them together. And when I do five plus seven, 29 I get positive 12. So our best answer is C.