Hello,

Can someone please show me how to complete this square?

2x^2+y^2=2y+1

Thanks!

-Mark

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- Nov 23rd 2009, 04:34 PMl flipboi lCompleting the square
Hello,

Can someone please show me how to complete this square?

2x^2+y^2=2y+1

Thanks!

-Mark - Nov 23rd 2009, 04:46 PMBacterius
You are sure it isn't in the right-hand side ? If yes, then it is easy, if no, then there is a little more thinking to do. Have you tried using square identities to factor out both unknowns together ?

- Nov 23rd 2009, 05:13 PMl flipboi l
- Nov 23rd 2009, 08:07 PMBacterius
I think there should be a way to factorize using a square identity, leaving alone a constant based on (since you are completing the square) :

I know what follows is not very mathematic but perhaps it could be a good idea to try with some numbers substituting and and investigate what happens, if a pattern doesn't show up ... but you have to find working numbers (Sweating) ...

Here is what I would do :

I would say , therefore :

Woah ! A square identity !

And I successfully completed the square.

Try with :

Erm ... we have to do some working there :

(substract 7 from both sides)

And then the magic operates :

Thus, it seems that regardless of what value takes, we always have , where is dependent on .

Basically, we know that (since we always take off the left-hand side just the needed amount to leave on the left-hand side)

Which simplifies to : , and finally, .

Now let's put it all together, and detail the steps more mathematically (what was shown up there was brainwork) :

But we need a little 1 on the left-hand side to successfully complete the square :

Finally :

I think that is what the book wants (Nod) - Nov 23rd 2009, 08:46 PMl flipboi l
Great stuff, Thank you!