Explanation for Question 8 From the Math (No Calc) Section on the 2019 May Sat
Questioning says, which of the following is a solution to the equation above. 2 So the first thing I noticed about this is that I'm going to have 3 to factor this. And I know that because there's a squared and X squared 4 in the original equation, which means that I'm going to have to put everything 5 on one side, all of the terms and then factor it. 6 I also noticed that I'm probably going to have to use the quadratic equation, 7 because if you notice a lot of the answer choices have a radical, 8 so I've gone ahead and I've written the formula just as a reminder to 9 the quadratic formula up at the top there. 10 Now we're going to start by just putting everything on one side. 11 So that would become two X squared, 12 two X squared plus negative two X plus negative five 13 is equal to zero. Um, 14 and just to make this easier to plug into the quadratic formula, 15 I'm going to actually divide everything by two now. 16 So that becomes X squared plus negative X plus negative 17 five. Over two is equal to zero. 18 And now I can plug this into the quadratic equation with a being equal 19 to one B being equal to negative one and C being 20 equal to negative five over two. 21 So let's start by doing that. The opposite of negative one is one. 22 So one plus or minus negative one squared is just 23 one. So one minus four times, 24 one times, negative five over two, 25 all over two times a, 26 which is just one. So that becomes two. Then we can simplify this into 27 one plus or minus negative 21 minus 28 negative 10 just becomes 11 over two. 29 And if you notice that's actually one of the answer choices D is one 30 plus 11 over two. 31 So in that case, in this case, that is the answer.