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!
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)
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.
To further simplify the expression 2 times the square root of 3 divided by 2, you can cancel out the common factor of 2 in the numerator and denominator. This gives you:
2 * sqrt(3) / 2
Since 2 divided by 2 is equal to 1, you are left with:
sqrt(3)
Therefore, the ultimate result for the expression 2 times the square root of 3 divided by 2 is simply sqrt(3).
So, after substituting the values and simplifying, the solutions to the quadratic equation x^2 - 10x + 22 = 0 using the quadratic formula are:
x = (10 + sqrt(3)) / 2
x = (10 - sqrt(3)) / 2