ive been studying for my math 10 test and i know everything pretty well exept "complete the square". you have a trinomial such as 9x^2-60x+k. find k
another example could be something like m^2+km+49. find k. another one is 4x^2+28x+k.please can anyone explain how to find this answer (preferably not trial and error). your help is appreciated, thank you
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Last edited by srv_king at Apr 23, 2008,
Basically, the coefficient of the middle term is the sum of the two factors of the last term. In the second example you gave, k has to be the sum of two numbers that when multiplied equal 49. Now, the only factors of 49 are 1,7,49 and their negatives, so k has to be the sum of two of those. Now since you're completing a square, 7 squared is 49, so k would be 14, and when factored, would come out to (m+7)(m+7). To check your answer, you can just use the FOIL method on your answer.

Edit: The first seems a little more difficult. Now, you don't know completely what you need, but you know it will come down to (3x-something)(3x-something). Now, you know that when you multiply this out, you'll have 9x^2-6xsomething+something^2. Now, you know the middle term is 60x, so that something has to be 10, since 6*x*10=60x. Then your final term has to be that something (10) squared, which is 100. I think this is correct and hopefully it helped a little.
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Last edited by lyingfromyou118 at Apr 23, 2008,