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.

 

[CellCoree]

I would say that there is nothing inherently wrong with completing the square in this way. In fact, completing the square is a mathematical technique that can be approached in different ways, and as long as the final result is correct, the method used is valid. However, it is important to understand the reasoning behind the steps and the underlying mathematical concepts involved in completing the square. This will help in solving more complex problems and understanding the concepts better. So, while this way may make more sense to you personally, it is still important to fully understand the traditional method of completing the square in order to build a strong foundation in mathematics.