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Algebra: How does [x^2 4x+41] become [(x^2+4x4)1] 
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#1
Aug3113, 01:28 PM

P: 300

If I want to complete the square with
[itex](x^{2}4x+3)[/itex] I would write [itex](x^{2}4x+(...) +3  (...)) = (x^{2}4x+4+34) = (x^{2}4x+41) = (x^{2}+4x4)  1[/itex] Why does adding the parentheses to separate the 1 change all the signs. I understand it has something to do with factoring out a negative, but how exactly? I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the 1 when completing the square for an integration problem in calculus? 


#2
Aug3113, 02:31 PM

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"I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the 1 when completing the square for an integration problem in calculus? "
It doesn't; you are perfectly correct concerning addition/subtraction relative to the associative property. The last expression is missing a minus sign in front of the parenthesis expression containing the completed square. 


#3
Aug3113, 09:59 PM

P: 62

(x^2+4x4)+7 ?



#4
Sep113, 04:43 AM

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P: 1,745

Algebra: How does [x^2 4x+41] become [(x^2+4x4)1]
There's a mistake, x^2 + 4x  4 is not a square.
The correct way to start is: x^2  4x + 3 (x^2 + 4x) + 3 


#5
Sep113, 08:28 PM

P: 62

If you start with (x^2+4x) + 3, you divide that 4 by two and square it, resulting in (x^2+4x+4)+3. However, you have do add that 4 to the outside, but doesn't the negative in the very front make it a negative 4, finally resulting in (x^2+4x+4) + 7? I'm confused on where to go from here. 


#6
Sep213, 01:14 PM

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Here is a more abstract example for you to practice the steps on: x^2 + px + q = 0 


#7
Sep213, 05:13 PM

P: 62

Think I got it:
(x+2)^2 + 7? :) 


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