SOLUTION: factor the quadratic expression completely, and find the roots of the expression. 66x2 - 130x + 56

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: factor the quadratic expression completely, and find the roots of the expression. 66x2 - 130x + 56       Log On


   

Question 481263: factor the quadratic expression completely, and find the roots of the expression.
66x2 - 130x + 56

Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
First factor out the common factor of 2
2%2833x%5E2-65x%2B28%29=0
Then find factors of (33*28) that add up to -65
The best way to do this is to break down the product into prime factors:
33*28 = 11*3*7*4
(11*3)+(7*4) = 33+28 = 61
(11*7)+(3*4)= 77+12 = 89
(11*4)+(3*7) = 44+21 = 65
This means we can split -65x into -44x -21x
Use factor by grouping
2%2833x%5E2-44x-21x%2B28%29=0
2%2811x%283x-4%29-7%283x-4%29%29=0
2%283x-4%29%2811x-7%29=0
To find the roots, first divide out the 2 **notice, it has no effect on the roots**
Then solve for each factored expression separately
3x-4+=+0
3x=4
x+=+4%2F3
11x-7+=0
11x=7
x+=+7%2F11
The two roots are x=4/3 and x=7/11