SOLUTION: the product of two consecuitive integers is 156. use the equation n(n=1)=156 to find the integers.

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Question 159408: the product of two consecuitive integers is 156. use the equation n(n=1)=156 to find the integers.

Answer by jim_thompson5910(28504) About Me  (Show Source):
You can put this solution on YOUR website!
n%28n%2B1%29=156 Start with the given equation


n%5E2%2Bn=156 Distribute


n%5E2%2Bn-156=0 Subtract 156 from both sides


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for n:


Starting with the general quadratic


an%5E2%2Bbn%2Bc=0


the general solution using the quadratic equation is:


n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve n%5E2%2Bn-156=0 ( notice a=1, b=1, and c=-156)





n+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A-156+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=-156




n+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A-156+%29%29%2F%282%2A1%29 Square 1 to get 1




n+=+%28-1+%2B-+sqrt%28+1%2B624+%29%29%2F%282%2A1%29 Multiply -4%2A-156%2A1 to get 624




n+=+%28-1+%2B-+sqrt%28+625+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




n+=+%28-1+%2B-+25%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




n+=+%28-1+%2B-+25%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


n+=+%28-1+%2B+25%29%2F2 or n+=+%28-1+-+25%29%2F2


Lets look at the first part:


x=%28-1+%2B+25%29%2F2


n=24%2F2 Add the terms in the numerator

n=12 Divide


So one answer is

n=12




Now lets look at the second part:


x=%28-1+-+25%29%2F2


n=-26%2F2 Subtract the terms in the numerator

n=-13 Divide


So another answer is

n=-13


So our solutions are:

n=12 or n=-13





So the first number is 12 and the second number is 13 (if you only want positive integers)


Or, the first number is -13 and the second number is -12 (if you don't mind negative numbers)