MHB What is x when c is at maximum?

[Wilmer]

a = x^2 + 2cx + 1
b = 2x + 3c + 3

a / b = 5 plus a remainder of 11.

c=?

Want to include above in a "puzzle" site.
Want see if it makes sense..

Can you solve it?
Than you.

 

[MarkFL]

...Can you solve it?...

Yes:

Spoiler

One easy solution is:

$$c=-10$$

I will be glad to show what I did if required.

 

[Wilmer]

Yes:

Spoiler

One easy solution is:
$$c=-10$$
I will be glad to show what I did if required.

Yippee! Yes, c=-10 (x=25) is a solution.

There are 6 solutions (I'm 99% sure) where c and x are integers (positive or negative).
3 of those have x and c > 0.

Hokay: question is now: what is x when c is at maximum?

Thanks Mark. Nice to hear from you !