Question 168742
consecutive integers follow the pattern x, x+1, x+2, etc



So "the prduct of two consecutive integers is 20" translates to {{{x(x+1)=20}}}



{{{x(x+1)=20}}} Start with the given equation



{{{x^2+x=20}}} Distribute



{{{x^2+x-20=0}}} Subtract 20 from both sides.



{{{(x+5)(x-4)=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+5=0}}} or  {{{x-4=0}}} 


{{{x=-5}}} or  {{{x=4}}}    Now solve for x in each case



So our answers are 


 {{{x=-5}}} or  {{{x=4}}} 



Which means that the two numbers are 


-5 and -4 


OR...



4 and 5