Would you please explain problem #13 on p.486, Test 2, in the new SAT book.

Sure. You’re going to want to use the quadratic formula here, since the quadratic doesn’t factor easily and this is in the no calculator section, so graphing is out of the question. First, divide everything by 2 to make the math a little easier:

    \begin{align*} 2m^2-16m+8&=0\\ m^2-8m+4&=0\end{align*}

Now put that into the quadratic formula.

    \begin{align*} m&=\dfrac{8\pm\sqrt{(-8)^2-4(1)(4)}}{2(1)}\\ m&=\dfrac{8\pm\sqrt{48}}{2}\\ m&=4\pm\dfrac{\sqrt{48}}{2}\end{align*}

At this point, note that you need not simplify further because the question asks for the sum of all values that satisfy the equation. There are two values: the + part of the ±, and the – part. Add them together, and everything after the ± goes away!


To see all the questions from the Official Tests that I’ve already explained, click here. I update that list every time I do a new explanation.

Comments (3)

Yo B, I’m tying to shoot you a question, but the site keeps asking me to join first. I’m already a free member yo. Can free members send you a question or I gotta pay you B?

How do you work question 11 in no calculator section of Test 4? x=2y+5 and y=(2x-3)(x+9) How many ordered pairs (x,y) satisfy the system of equations shown above? A. 0 B. 1 C. 2 D. Infinitely many
The CB explanation looks whack yo! I just see a line and a parabola that only cross each other twice.

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