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**atran****Member**- Registered: 2013-07-12
- Posts: 91

Hi again, this question may seem silly, but I'm confused.

Say, (x^2)+6x-4=0, then by completing the square I get:

(x^2)+6x-4= 0

(x^2)+6x = 4

(x^2)+6x+9= 4+9

(x+3)^2= 13

Now, why isn't sqrt((x+3)^2) also equal to -(x+3)=-x-3?

Many small questions have been popping up in my head. This is leading me to a confused state. I used to do well and understand algebra, but I don't what happened, things started becoming confusing and unclear.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi atran;

It is usually written like this but you are essentially correct.

(x+3)^2 = 13

(x+3) = ±√13

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**atran****Member**- Registered: 2013-07-12
- Posts: 91

So there are four ways of expressing it?

1) x+3=√13 => x=√(13)-3

2) -(x+3)=-√13 => x=√(13)-3

3) x+3=-13 => x=-√(13)-3

4) -(x+3)=√13 => x=-√(13)-3

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

That is only two distinct ways.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**atran****Member**- Registered: 2013-07-12
- Posts: 91

I still don't get it. I learned that √(x) or x^(1/2) is the principal square root of x.

How to think when getting from this step [(x+3)^2 = 13] to [(x+3) = ±√13]?

I mean, why the last step is written like that? Why not (±(x+3)=√13)?

What makes both (±(x+3)=±√13) and (∓(x+3)=±√13) valid?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

I still don't get it. I learned that √(x) or x^(1/2) is the principal square root of x.

Who says you should only use the principal root in this case. That would only get one root, a quadratic has 2 roots. See post #2

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**math.guru.92****Member**- Registered: 2013-07-25
- Posts: 3

It is simple. Here we are dealing with the polynomial of degree "2" so when we will take a an under root on both sides, we will find two solutions of x one with a positive sign and one with negative sign.

(x+3)^2 = 13 ---------- original

when we take under root we get two equations

(x+3) = +√13 ----(equation 1) (x+3) = -√13 ------- (equation 2)

equation 1 goes to form equation 2 goes to form

x=+√13 - 3 x=-√13 -3

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