SOLUTION: Find two negative consecutive integers whos product is 272.

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Question 701784: Find two negative consecutive integers whos product is 272.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
ONE WAY:
272=2^4*17=16*17
so the two integers are highlight%28-16%29 and highlight%28-17%29.

QUADRATIC WITH FACTORING WAY:
Let n and n-1 be those integers
n%28n-1%29=272 --> n%5E2-n=272 --> n%5E2-n-272=0
Factoring, the equation is re-written as %28n-17%29%28n%2B16%29=0
with solutions n=17 (discarded because it's not a negative number),
and
n=highlight%28-16%29 --> n-1=16-1=highlight%28-17%29.

QUADRATIC WITH QUADRATIC FORMULA
Let x and x%2B1 be those integers
x%28x%2B1%29=272 --> x%5E2%2Bx=272 --> x%5E2%2Bx-272=0
The coefficients are
a=1 for the invisible 1 in front of x%5E2
b=1 for the invisible %281%29 on front of x
and c=-272
The quadratic formula is x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
so substituting the a, b and c values we get

That leads us to
x=%28-1-33%29%2F2 --> x=-34%2F2 --> x=highlight%28-17%29 --> x%2B1=-17%2B1 --> x%2B1=highlight%28-16%29,
and x=%28-1%2B33%29%2F2 --> x=32%2F2 --> x=16 (discarded because it's not a negative number).