SOLUTION: Please help me solve this. The product of two consecutive integers is equal to ten times the smaller integer minus eight. Find the integers.

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Question 306638: Please help me solve this. The product of two consecutive integers is equal to ten times the smaller integer minus eight. Find the integers.
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
let the numbers be x & x+1
product of both = x(x+1)
x(x+1)= 10x-8
x^2+x=10x-8
x^2-8x+9=0
x^2-9x+x-9=0
x(x-9)+1(x-9)=0
(x-9)(x+1)=0
x= 9 OR -1

Answer by MathTherapy(10551) (Show Source):
You can put this solution on YOUR website!
Please help me solve this. The product of two consecutive integers is equal to ten times the smaller integer minus eight. Find the integers.

Let the smaller integer be S

Then the larger consecutive integer is S + 1, and their product is S(S + 1)

Now, since their product is equal to ten times the smaller integer minus eight, then we'll have: S(S+ 1) = 10S - 8

(S - 8)(S - 1) = 0

Therefore, S, or the smaller integer = or , which means that the two consecutive integers are either and or and .