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# Completing square? watch

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1. The question is:
The function f is given by f: x-> 7-12x-4x^2, x E R
a) Find the values of the positive constants A, B and C for which:
A-(Bx+C)^2=7-12x-4x^2

I did as follows:
LHS:
7-12x-4x^2
=-4[x^2+12x-7/4]
=-4[x^2+12x+36-36+7/4]
=-4[(x+36)^2-151/4]
=-4(x+6)^2+151
=151-4(x+6)^2

This isn't in the form A-(Bx+C)^2 (because of the -4 before (x+6) bracket) and the answers are wrong. What did I do wrong? Am I supposed to complete square?
2. Your mistake is in the 2nd line- it should be:

-4[x^2+3x-(7/4)]
3. In regard to trying to get the answer in that form, you have to be able to spot a little thing.
Firstly, by completing the square, you should get:

23 - 4(x+2)^2

Notice that 4 = 2^2

= 23 - (2^2)(x+2)^2

Now, you can group the '2' and the (x+2), and square the whole thing

= 23 - [2(x+2)]^2

= 23 - (2x+4)^2
4. Thanks for your quick help. I got -4x^2-12x+7 when I completed square, which gave A=16, B=2, C=3. That's a bit clever to notice the 2^2 part!

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Updated: December 26, 2004
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