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

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Find two consecutive odd integers whose product is 79 more than their sum.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 111427: Find two consecutive odd integers whose product is 79 more than their sum.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive odd integers follow the form: 2x%2B1, 2x%2B3, etc


So the product of two such integers is 79 more than their sum translates to: %282x%2B1%29%282x%2B3%29=%282x%2B1%29%2B%282x%2B3%29%2B79

4x%5E2%2B8x%2B3=%282x%2B1%29%2B%282x%2B3%29%2B79 Foil the left side


4x%5E2%2B8x%2B3=4x%2B83 Combine like terms


4x%5E2%2B8x%2B3-4x-83=0 Get everything to one side


4x%5E2%2B4x-80=0 Combine like terms


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 4%2Ax%5E2%2B4%2Ax-80=0 ( notice a=4, b=4, and c=-80)





x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A4%2A-80+%29%29%2F%282%2A4%29 Plug in a=4, b=4, and c=-80




x+=+%28-4+%2B-+sqrt%28+16-4%2A4%2A-80+%29%29%2F%282%2A4%29 Square 4 to get 16




x+=+%28-4+%2B-+sqrt%28+16%2B1280+%29%29%2F%282%2A4%29 Multiply -4%2A-80%2A4 to get 1280




x+=+%28-4+%2B-+sqrt%28+1296+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-4+%2B-+36%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-4+%2B-+36%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%28-4+%2B+36%29%2F8 or x+=+%28-4+-+36%29%2F8


Lets look at the first part:


x=%28-4+%2B+36%29%2F8


x=32%2F8 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%28-4+-+36%29%2F8


x=-40%2F8 Subtract the terms in the numerator

x=-5 Divide


So another answer is

x=-5


So our solutions are:

x=4 or x=-5





Now plug in x=4

2%284%29%2B1=9 and 2%284%29%2B3=11

So one pair of numbers is 9,11

Now plug in x=-5

2%28-5%29%2B1=-9 and 2%28-5%29%2B3=-7

So another pair of numbers is -7,-9