Question 120420
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(x+1)=156}}}



{{{x^2+x=156}}} Distribute



{{{x^2+x-156=0}}} Subtract 156 from both sides



{{{(x+13)(x-12)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+13=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+1=-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*-12=156}}}



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