Is there anything wrong with completing the square this way?

  • Context: High School 
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Discussion Overview

The discussion revolves around the method of completing the square for the quadratic expression 3x^2 + 12x + 27. Participants explore different approaches to this technique and express their preferences for the method used.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents a method of completing the square that involves factoring out a coefficient and rearranging terms, which they find more intuitive.
  • Another participant agrees with this method, stating that it works fine and suggests verifying by expanding the expression to confirm equivalence.
  • A third participant mentions that they have always used a similar approach when dealing with coefficients of x^2.
  • One participant acknowledges the correctness of the method but raises the possibility that a teacher might prefer a different method for instructional purposes.

Areas of Agreement / Disagreement

Participants generally agree that the method presented is valid, but there is an acknowledgment of potential differences in teaching methods that could lead to confusion.

Contextual Notes

There is a lack of consensus on the preferred method of teaching completing the square, and the discussion does not resolve whether one method is superior to another.

Joked
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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.
 
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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.
 
That is, frankly, the way I have always handled coefficients of [itex]x^2[/itex].
 
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.
 

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