SOLUTION: the product of a negative integer and 5 less than twice the integer equals the integer plus 56. find the integer.

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Question 981317: the product of a negative integer and 5 less than twice the integer equals the integer plus 56. find the integer.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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x=negative integer
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%28x%29%282x-5%29=x%2B56
2x%5E2-5x=x%2B56 Subtract (x+56) from each side.
2x%5E2-6x-56=0 Divide each side by 2.
x%5E2-3x-28
%28x-7%29%28x%2B4%29=0
x-7=0 OR x%2B4=0
x=7 OR x=-4
Since we are looking for a negative integer,
ANSWER: The negative integer is -4.
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CHECK:
(x)(2x-5)=x+56
(-4)(2(-4)-5)=-4+56
(-4)(-8-5)=52
(-4)(-13)=52
52=52