SOLUTION: If one of the two roots of the equation (14x - 5)(7x - 3) + ax - 17 = 0 is -1/2 , what is the other root?

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Question 1089869: If one of the two roots of the equation (14x - 5)(7x - 3) + ax - 17 = 0 is -1/2 , what is the other root?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If one of the two roots of the equation
%2814x+-+5%29%287x+-+3%29+%2B+ax+-+17+=+0+is -1%2F2 ,than first ind a
%2814%28-1%2F2%29+-+5%29%287%28-1%2F2%29+-+3%29+%2B+a%28-1%2F2%29+-+17+=+0+
%28-7+-+5%29%28-7%2F2+-+6%2F2%29+%2B+a%28-1%2F2%29+-+17+=+0+
%28-7+-+5%29%28-13%2F2%29+%2B+a%28-1%2F2%29+-+17+=+0+
78+%2B+a%28-1%2F2%29+-+17+=+0+
61++-a%2F2++=+0+
61++=+a%2F2+
a=122+
%2814x+-+5%29%287x+-+3%29+%2B+122x+-+17+=+0+......factor completely
98x%5E2+-+77+x+%2B+15%2B+122x+-+17+=+0+
98x%5E2+%2B+45x+-+2+=+0+
98x%5E2+%2B+45x+-+2+=+0+
%282x+%2B+1%29+%2849x+-+2%29+=+0
roots:
if %282x+%2B+1%29++=+0->x=-1%2F2(given)
if %2849x+-+2%29+=+0->x=2%2F49
so, the other root is 2%2F49