SOLUTION: I don't understand this problem because I have to find negative integers. The problem says "Find two consecutive, negative integers whose product is 156." Could you please help me?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I don't understand this problem because I have to find negative integers. The problem says "Find two consecutive, negative integers whose product is 156." Could you please help me?      Log On


   

Question 120420: I don't understand this problem because I have to find negative integers. The problem says "Find two consecutive, negative integers whose product is 156." Could you please help me?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive integers are integers that are adjacent to each other on the number line. So numbers like 1,2,3,4, are consecutive integers. So consecutive integers follow the algebraic form x,x+1,x+2, etc...


Since the product of 2 consecutive integers is 156, this means

x%28x%2B1%29=156


x%5E2%2Bx=156 Distribute


x%5E2%2Bx-156=0 Subtract 156 from both sides


%28x%2B13%29%28x-12%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x%2B13=0 or x-12=0

x=-13 or x=12 Now solve for x in each case


So our answers are
x=-13 or x=12


Since the question asked for "two consecutive, negative integers", this means the only solution is x=-13


So our first integer is -13


Now to find the next integer, simply add one to -13 to get

-13%2B1=-12

So our second integer is -12


So the two consecutive, negative integers are: -13 and -12


Check:

To verify this answer, simply multiply -13 and -12 to get

-13%2A-12=156


Since the product of -13 and -12 is 156, this verifies our answer.