Posted by **Corinna** on Saturday, October 10, 2009 at 10:46am.

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!

- Algebra -
**drwls**, Saturday, October 10, 2009 at 12:00pm
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**, Saturday, October 10, 2009 at 12:06pm
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)

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