SOLUTION: Find two consecutive odd integers whose product is 79 more than their sum.

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Question 111427: Find two consecutive odd integers whose product is 79 more than their sum.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Consecutive odd integers follow the form: , , etc

So the product of two such integers is 79 more than their sum translates to:

Foil the left side

Combine like terms

Get everything to one side

Combine like terms

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=4, b=4, and c=-80

Square 4 to get 16

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 4 to get 8

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

Now plug in

and

So one pair of numbers is 9,11

Now plug in

and

So another pair of numbers is -7,-9