SOLUTION: Why can't(-9+ sqrt(21))/6 be simplified further if all 3 numbers are multiples of three? Shouldn't you get "-3+7, which gives you 4 from dividing the numerator by 6? or at least 9+

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Why can't(-9+ sqrt(21))/6 be simplified further if all 3 numbers are multiples of three? Shouldn't you get "-3+7, which gives you 4 from dividing the numerator by 6? or at least 9+      Log On


   

Question 877951: Why can't(-9+ sqrt(21))/6 be simplified further if all 3 numbers are multiples of three? Shouldn't you get "-3+7, which gives you 4 from dividing the numerator by 6? or at least 9+ sqrt(7)/2? By the way the question is (3x+3)(x+2)=1 solve by quadratic formula. The help would be much obliged.
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The reason is because of that square root. If you had -9+21 over 6, then you can factor out 3. However, that 21 is buried in a root, so you can't factor out 3 from it.

I guess you could say this

-9%2Bsqrt%2821%29=-9%2Bsqrt%283%2A7%29

-9%2Bsqrt%2821%29=-9%2Bsqrt%283%29%2Asqrt%287%29

but that's about it and it's not a good step in terms of simplifying

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So I'd stick with the answers of

x+=+%28-9%2Bsqrt%2821%29%29%2F6 or x+=+%28-9-sqrt%2821%29%29%2F6

you can condense them into one single equation

x+=+%28-9%2B-sqrt%2821%29%29%2F6

Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
(-9+ sqrt(21))/6
%28-9%2B+sqrt%2821%29%29%2F6 cannot be simplified because the terms of the numerator cannot be combined without approximation, and because all three separate numbers have no factors in common. Stated more plainly, -9 and sqrt(21) and 6 have no common factor.

Do not confuse the square root with the input of the square root. Seven is not a factor of sqrt%2821%29.