Question

The product of two consecutive odd integers is 9 more than 10 times the smaller integer. Find the pair of integers.

I have done all the work but can't figure out how to find the final answer.

I did x * x + 1 = 10x + 9
x^2 - 9x - 9 = 0

I factored to get (x + 1)(x - 9) so x = -1 and x = 9

But I don't understand how to answer the exact question.

Answer 1

That's why it is important to define your variables.

It looks like you called the first number x, and the next consecutive integer should have been
x + 2, instead of x+1
furthermore, your factors don't come out to your equation if expanded.

so x(x+2) = 10x + 9
x^2 + 2x = 10x + 9
x^2 - 8x - 9 = 0
(x - 9)(x + 1) = 0
x = 9 or x = -1

case1 :
your two odd integers are 9 and 11
check: product = 99
which is 10(9) + 9, so that one works

case2:
your two odd integers are -1 and 1
check: product = -1
which is 10(-1) + 9, so that one works as well

answer:
the pair of integers are either, 9 and 11 OR they are -1 and +1