Posted by Corinna on .
Solve x^210x+22=0 by using the quadratic formula. After I substituted in the values for A, B, and C, and broke it down I got 10 plus or minus 2 times the square root of three/2. How do you break this down further? I know ten can be divided by 2 to get five, and 2/2 is 1, but how do you handle the sq. of 3 divided by 2? What would the ultimate result be? Thank you!

Algebra 
drwls,
B^2  4AC = 12
x = [10 +/ sqrt12]/2
= 5 +/ (2*sqrt3)/2
= 5 +/ sqrt3 = 6.732 or 3.268
That is all the simplification you can to. 
Algebra 
jim,
Well done! You got it right. But I think you may have missed a turn in the simplification.
The simplification is largely a matter of taste, but also laziness  the less you have to write to use your result in the next stage of a problem, the better :)
You started with:
(10 +/ sqrt(12))/2
sqrt(12) = sqrt(4)*sqrt(3) = 2sqrt(3)
so (10 +/ sqrt(12))/2 =
(10 +/ 2sqrt(3)) /2
= 10/2 +/ 2sqrt(3)/2
= 5 +/ sqrt(3)