anonymous
  • anonymous
How does (x^2 -2x) + (y^2+4y)=7 become (x^2-2x+1)+(y^2 +4y+4)=7+1+4? Where specifically do the 1 and 4 come from?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
the 1 and the 4 in the right side came from completing the square on the left side.
anonymous
  • anonymous
So, how do you complete the square?
anonymous
  • anonymous
(x^2 - 2x + ???) what needs to be in place of ??? in order (no pun) to write in this form: (x - #)^2

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More answers

anonymous
  • anonymous
the procedure is to take half the coefficient of the linear term (the x-term), which is half of the 2 then square it... and that's what you add. here's an example..
anonymous
  • anonymous
|dw:1333189900951:dw|
anonymous
  • anonymous
Oh. OK. that makes more sense :)
anonymous
  • anonymous
so do you see where the 4 came from?
Mimi_x3
  • Mimi_x3
You can use the formula to complete the square. \[x^{2}+bx = \left(x+\frac{b}{2}\right) ^{2} -\left(\frac{b}{2}\right) ^{2} \] \[x^{2} -bx = \left(x-\frac{b}{2}\right) ^{2} -\left(\frac{b}{2}\right) ^{2} \]
anonymous
  • anonymous
thank you! ;D
anonymous
  • anonymous
np
anonymous
  • anonymous
@order this is what you're going to do.... \[\Large (x^2-2x+1)-1+(y^2+4y+4)-4=7\] just take number before x and y and divide by 2 then square them... in your case you have... -2 and 4 , when you divide them by 2 they become.. -1 and 2 ... now when you square them they become... 1 and 4 Now add 1 and -1 to complete the square .. do the same with 4 and -4 ...(why + and -?) because, 4-4=0 and -1+1=0 so the value of equation doesn't change... Once you've added them... Equation becomes like I wrote at principal... then move -1 and -4 to the right side and you'll get 7+4+1 and the left sides converts into \[\Large (x-1)^2+(y+2)^2=7+4+1\] Got it ??
anonymous
  • anonymous
written in this form as @Kreshnik wrote it, you can easily see it is the equation of a ....??? what?
anonymous
  • anonymous
Of a circle.
anonymous
  • anonymous
nice. :)
anonymous
  • anonymous
correct !
anonymous
  • anonymous
Thanks so much!! :D This is great.

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