VVoidSmiley69

Sorry I am not 100% how to explain this but basically by completing the square, we can eventually put the equation in vertex form, which in this case will give us the maximum. In this the equation became -1(x+27.5)^2+765.25. So we know that 765.25 is the maximum.

Essentially, we just complete the square so we can easily fine the vertex through vertex form.

Yup I get. Thanks for this post, it really made cheater realize their loss of learning. They are also losing money by only looking for answers, hope they can learn.

It means to bring the variable on one side and to the constants on the other side essentially.

I will admit I have done this a few times, but i am mostly looking for the steps, I really don't care if I get 5/7 or a 3/7, I only want to learn the content, and sometimes teh message boards dont help. I think thats why many kids come here including myself sometimes come here to ask for help, while others only want answers. I understand your point, maybe people could ask for starting points instead of direct answers? 

For the maximum, I started off by adding up all the integers. 1+2+3...+10=55. 

So with that I gave a variable to each group, x and y.

Thus, x+y=55, then I switched that to a slope intercept form, so y= -x+55

So that gave me P= y * x, which I then simplified to P= x* (-x+55), which became -(x^2-55x)

Then we can complete the square to get -(x^2-55x+765.25), and that simplified is -(x-27.5), so 27.5* 27.5 will give us the highest number, but since we only have intergers we can go +1 and -1 to get 27*28 and that will equal 756.

How can I find the minimum with completing the square? Thats the part I dont understand.

Thanks Melody, this answer als provides me a different insight the problem. 

Thanks a lot Geno, I clearly understand the problem now. :)

Sorry I am new to Latex, I will try not to do it again :)