Will this equation ever be negative (proof)
I have a discrete math assignment which says:
Is the following statement true or false? Explain.
For any real numbers x, y, the number 9x2 + 4y2 + 6xy − 3x − 2y + 1 is not negative.
I am pretty sure that this is true (I wrote a program that went through a lot of the possibilities and it was never negative). However, I do not have a vigorous proof that this is true. If anyone can help me get started on this proof it would be great. I talked to my prof and he said the best way was to not break it into cases, and that the other way is really easy. I apparently just can't see it. Thanks in advance for anyones help into this. I do not necessarily want the proof done for me, but even an idea where to start would be great.