Algebra, 6th Edition, Page 161

[LiliiaG24]

If x²+8x+13=0, what is x?

x=-8±√8²-4(1)(13)/2(1)=-8±√64-52/2(1)=-4±√12/2=(-4+√3, -4-√3)

How did you get -4±√12/2 please? As I am getting -8±√64-52/2(1)=-8±√12/2=-8±√3x4/2=-8±2√3/2=(-3√3;-5√3). Where is my mistake? Thanks.

[RonPurewal]

in the quadratic formula, EVERYTHING is divided by '2a'.
i.e., the entire expression (-b ± √(b^2 - 4ac)) is divided by 2a. not just the square-root term.

[RonPurewal]

...and there's also another issue, which is that you can't add integers to square roots.

e.g., if you have 10 – 6√2, then that's just ... 10 – 6√2. it is NOT 4√2.
there is nothing that can be done to 'simplify' this expression—exactly as it is impossible to simplify, say, 10 – 6π or 10 – 6x.

[RonPurewal]

finally, it's interesting that this is even in the practice sets in the first place, because there has never been an official GMAT problem requiring the quadratic formula.
literally, never.

yes, the quadratic formula is mentioned in the 'math review' part of the OG, but that part also mentions several other concepts that have never been tested (e.g., how to calculate a standard deviation).

on the other hand, this particular instance is a pretty good indicator of whether you can /1/ work with formulas and /2/ correctly manipulate expressions involving roots.
you made mistakes in both of those areas (as explained above), so that's where you should pay attention here.