SOLUTION: the product of two negative consecutive integers is 56. Find the integer

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Question 712953: the product of two negative consecutive integers is 56. Find the integer
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive integers are integers that follow in sequence, each number being 1 more than the previous number, represented by n, n+%2B1, n+%2B+2,+n+%2B+3, ..., where n is any integer.
in your case we have two negative consecutive integers; so, let them be n and n+%2B1
their the product is 56; so, we have
n%28n+%2B1%29=56
n%5E2+%2Bn=56
n%5E2+%2Bn-56=0.......use quadratic formula to solve for n
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
n+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-56%29+%29%29%2F%282%2A1%29+
n+=+%28-1+%2B-+sqrt%28+1%2B224%29%29%2F2+
n+=+%28-1+%2B-+sqrt%28+225%29%29%2F2+
n+=+%28-1+%2B-+15%29%2F2+...we will need only negative solution for n
n+=+%28-1+-+15%29%2F2+
n+=+%28-16%29%2F2+
highlight%28n+=+-8+%29...first number
n+%2B1=-8%2B1=highlight%28-7%29...second number