Completing the square for x^2 - 9x

L3

New member
Joined
Sep 11, 2007
Messages
21
This is probably going to be a very silly question but I feel very confused.

The math problem is,
Rename x[sup:18fmecll]2[/sup:18fmecll] - 9x as an expression involving a perfect square trinomial.

So I did,

x[sup:18fmecll]2[/sup:18fmecll] -9x =
x[sup:18fmecll]2[/sup:18fmecll] -9x + (-9/2)^2 - (-9/2)^2
(x - 9/2)[sup:18fmecll]2[/sup:18fmecll] - (-9/2)[sup:18fmecll]2[/sup:18fmecll]

And this is where I hit the snag. The answer is (x - 9/2)[sup:18fmecll]2[/sup:18fmecll] - 81/4.

Which does makes sense if it is (-9/2)[sup:18fmecll]2[/sup:18fmecll], since (-9)[sup:18fmecll]2[/sup:18fmecll] is 81, but what I don't understand is why the negative would be with the 9 in the Parentheses. I mean when I wrote out the problem above I put in it, just so I could keep track of all the negatives. But how does one know it's supposed to be there.

I have this vague idea of almost being able to get it, I mean it is negative 9 over two, and therefore it would make sense if you times the fraction by the power of two that that would probably include the negative. But I keep writing out this post, thinking I get it, deleting the whole thing and then having second doubts and writing the whole thing out again. I just want to make certain that I understand. I have the lot of trouble in completing the square problems with negatives and positives, I keep getting quite muddled up. *sighs*.
 
L3 said:
This is probably going to be a very silly question but I feel very confused.

The math problem is,
Rename x[sup:3m95hfnf]2[/sup:3m95hfnf] - 9x as an expression involving a perfect square trinomial.

So I did,

x[sup:3m95hfnf]2[/sup:3m95hfnf] -9x =
x[sup:3m95hfnf]2[/sup:3m95hfnf] -9x + (-9/2)^2 - (-9/2)^2
(x - 9/2)[sup:3m95hfnf]2[/sup:3m95hfnf] - (-9/2)[sup:3m95hfnf]2[/sup:3m95hfnf]

And this is where I hit the snag. The answer is (x - 9/2)[sup:3m95hfnf]2[/sup:3m95hfnf] - 81/4.

Which does makes sense if it is (-9/2)[sup:3m95hfnf]2[/sup:3m95hfnf], since (-9)[sup:3m95hfnf]2[/sup:3m95hfnf] is 81, but what I don't understand is why the negative would be with the 9 in the Parentheses. I mean when I wrote out the problem above I put in it, just so I could keep track of all the negatives. But how does one know it's supposed to be there.It shouldn't be there. That negative sign you put there for your book-keeping. In actual derivation, it is not used.

I have this vague idea of almost being able to get it, I mean it is negative 9 over two, and therefore it would make sense if you times the fraction by the power of two that that would probably include the negative. But I keep writing out this post, thinking I get it, deleting the whole thing and then having second doubts and writing the whole thing out again. I just want to make certain that I understand. I have the lot of trouble in completing the square problems with negatives and positives, I keep getting quite muddled up. *sighs*.
 
L3 said:
… what I don't understand is why the negative would be with the 9 in the Parentheses …


It's because b is -9.

Since b = -9, we write (b/2)^2 as (-9/2)^2.

If you were completing the square on x^2 + 9x, instead, then b is +9, and there would be no negative sign.

 
Top