Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Completing the square

Hey everyone! I haven't been on for a while but I need someone to check this please!

Solve by completing the square:

x²-49=0

I wasn't sure what to do, as it doesn't look like a normal completing the square question, so I added in a 0x...

Thanks

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Completing the square

Yes, that's a bit of a strange question. The whole point of completing the square is to get rid of the x term, but if there isn't one then you have nothing to do.
It's certainly the right answer, anyway.

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Why did the vector cross the road?
It wanted to be normal.

Maelwys

Member

Registered: 2007-02-02

Posts: 161

Re: Completing the square

Yeah, that's a weird question. Personally, I'd just solve it by inspection, but that probably doesn't work for a class. Since your 0x looks a bit funny, it'd probably also be acceptable to just drop it and use the following:

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Completing the square

also, to both you maelwys and daniel,

doesn't mean ±7, it means just positive 7, the root sign '√' means the principal root, so you should really have x = ±√49 = ±7

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The Beginning Of All Things To End.
The End Of All Things To Come.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Completing the square

Actually luca i would have used '±' but I didn't know how to write it using Latex! I have another little query, is x²-1 simpler than (x+1)(x-1)?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Completing the square

I'm not sure, but I'd say yes. To work out x²-1, you need to find x² and then take 1.
To find (x+1)(x-1), you need to find x+1, and x-1 and then multiply them.

So x²-1 has two steps instead of 3. In almost all other cases though, factorising is a very good way to simplify things.

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Why did the vector cross the road?
It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Completing the square

Ok thanks mathsy

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Completing the square

It depends what you mean by simpler.  There are two simplified forms, expanded and factored.  I'd lean towards factored myself, the (x+1)(x-1) because it shows that roots.  But anyone can argue for expanded, x^2-1, just a well.

\pm:

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Completing the square

Aah ok thanks

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Completing the square

Or ":plusmn" if you want it outside [math] tags.

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Why did the vector cross the road?
It wanted to be normal.