Question 828432

The product of two consecutive odd integers is 22 more than 7 times the larger number. Use a quadratic equation to determine the two integers. 

I was thinking it would look something like:
x(2+x) = 22 + 7(2+x)
x (2 +x) - 7(2+x)-22 = 0
x^2 + 9 - 36
which you would then factor to get the two numbers. The answer is 9 and 11. I am not sure how you get this answer. Thank you for your help!
<pre>
You're correct up to here: x(2 + x) - 7(2 + x) - 22 = 0
{{{2x + x^2 - 14 - 7x - 22 = 0}}} ----- Distributing
{{{x^2 + 2x - 7x - 14 - 22 = 0}}} ----- COLLECTING like-terms
{{{x^2 - 5x - 36 = 0}}} ------ COMBINING like-terms

Solving this quadratic equation should result in x either being {{{highlight(9_or_- 4)}}}

Note that x CANNOT be - 4, since the problem states that the integers are odd, and - 4 is NOT ODD. Therefore,
the solution, x = - 4 is ignored.

Since x, in this case is the smaller integer, and is 9, then other odd integer = 9 + 2, or 11. 

Odd integers: {{{highlight_green(9_and_11)}}}
You can do the check!! 

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