SOLUTION: If the one of the two roots of the equation (2x - 7)(3x + 5) + ax + 31 = 0 is -4, what is the other root?

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Question 1089867: If the one of the two roots of the equation (2x - 7)(3x + 5) + ax + 31 = 0 is -4, what is the other root?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%282x+-+7%29%283x+%2B+5%29+%2B+ax+%2B+31+=+0
if one root is -4, we have
%282%28-4%29+-+7%29%283%28-4%29+%2B+5%29+%2B+a%28-4%29+%2B+31+=+0
%28-8+-+7%29%28-12+%2B+5%29+-4a+%2B+31+=+0
%28-15%29%28-7%29+-4a+%2B+31+=+0
105+-4a+%2B+31+=+0
+-4a+%2B+136+=+0
+4a+=+136+
+a+=+34+

%282x+-+7%29%283x+%2B+5%29+%2B+34x+%2B+31+=+0
6x%5E2+-+11x+-+35+%2B+34x+%2B+31+=+0
6x%5E2%2B+23x+++-+4++=+0
6x%5E2%2B+24x-x+++-+4++=+0
%286x%5E2%2B+24x%29-%28x+%2B+4+%29+=+0
6x%28x%2B+4%29-%28x+%2B+4+%29+=+0
%286x-1%29%28x+%2B+4+%29+=+0
roots:
if %286x-1%29+=+0->x=1%2F6
if %28x+%2B+4+%29+=+0->x=-4(given)
so, the other root is x=1%2F6