Is there anything wrong with completing the square this way?

[Joked]

3x^2 + 12x + 27
/3 /3 /3

3(x^2 + 4x + 9),

3(x^2 + 4x + 4 + 9 - 4)

(x^2 + 4x + 4) = (x+2)^2

3((x + 2)^2 +5)


This way is different then how it was taught to me but this way makes more sense to me.

 

[Cadaei]

Nope, works just fine. I actually prefer it that way. The idea is that, surely:

3(x^2 + 4x + 4 + 9 - 4) is equal to 3(x^2 + 4x + 9)

If you ever have any doubts, expand it out again. If you get the same thing back, you know you're fine.

 

[HallsofIvy]

That is, frankly, the way I have always handled coefficients of x^2.

 

[Diffy]

Yup that is correct. I wonder what prompted the question.

I guess the only way that could be incorrect is if a teacher was showing a different method and testing specifically on the knowledge that different method.