SOLUTION: please help me solve this problem: {{{find two consecutive numbers whose product is 72}}}

Question 912341: please help me solve this problem:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Better is you not use rendering tags for the description.

"find two consecutive numbers whose product is 72"

You should remember the basic multiplication fact, . Knowing this, you can do the algebra exercise and know in advance if your result is wrong or correct.

Two number, x and x+1. You assume x is an integer, probably a whole number.

You then hope to be able to factorize the trinomial left member, and knowing your basic multiplication facts, you find that 8 and 9 are good choices to start with so....
(x-8)(x+9)=0 seems to work.

Your description uses, "consecutive numbers", which could possibly be INTEGERS, meaning POSITIVE AND NEGATIVE WHOLE NUMBERS.

Looking just first for solutions to x,
x=8 OR x=-9.

Now, you want to evaluate the consecutive number.
For x=8, the next number is 9.
For x=-9, the next number is -8.

You then really have TWO possible answers.
The numbers you want are 8 and 9
OR
The numbers you want can be -9 and -8.

Those are your TWO SOLUTIONS.
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