SOLUTION: The product of two consecutive integers is 11 more than their sum. Find the integers. I have tried to solve this but i can't, the way the book explains it is very confusing.

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Question 335725: The product of two consecutive integers is 11 more than their sum. Find the integers. I have tried to solve this but i can't, the way the book explains it is very confusing.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first integer be x, then the next consecutive integr is x+1
x%2A%28x%2B1%29+=+x%2B%28x%2B1%29%2B11 " The product of two consecutive numbers is 11 more than their sum." Simplify this equation.
x%5E2%2Bx+=+2x%2B12 Subtract 2x from both sides.
x%5E2-x+=+12 Now subtract 12 from both sides.
x%5E2-x-12+=+0 Factor this trinomial.
%28x%2B3%29%28x-4%29+=+0 Apply the zero product rule.
x%2B3+=+0 or x-4+=+0 therefore...
x+=+-3 or x+=+4 these are the two integers.
Check:
x%2A%28x%2B1%29+=+x%2B%28x%2B1%29%2B11 Substitute x = 4.
4%2A%285%29+=+4%2B%285%29%2B11
20+=+9%2B11
20+=+20
You can check x = -3 yourself.