Question

Solve x^2-10x+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!

Answer 1

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.

Answer 2

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)