anonymous
  • anonymous
make the expression a perfect square.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
y^2+4y+
anonymous
  • anonymous
\[y ^{2}+4y+\]
anonymous
  • anonymous
need help

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anonymous
  • anonymous
okay... so, this is just a matter of understanding how polynomials work... there is a geometric interpretation that is easy to follow, but it would be hard to communicate over open study... instead the following might be helpful. expand the following: \[(x + \frac{ 1 }{ 2 }a)^2\]
anonymous
  • anonymous
yeah i dont get it
anonymous
  • anonymous
okay... did you try expanding the equation I gave you?
anonymous
  • anonymous
\[(x + \frac{1}{2}a) (x + \frac{1}{2}a)\] \[= x^2 + ax + (\frac{1}{2}a)^2\] In the case of your equation, what would a be?
anonymous
  • anonymous
ok i see what u mean
anonymous
  • anonymous
yeah! so the idea of completing the square is getting your equation from the form: y^2 + ay + ? to (y + ?)^2
anonymous
  • anonymous
the trick is finding the amount that you add to your first equation... this amount then determines what the value is going to be in the second equation. As it turns out, this all depends on what the value of a is.
anonymous
  • anonymous
if you ignore the last term in the last equation I gave you, you get \[x^2 + ax\] compare it to your equation: \[y^2 + 4x\]
anonymous
  • anonymous
so in this case, your a = 4. Using the last equation I gave you, what is the amount you need to add to your equation given a=4?
anonymous
  • anonymous
2?
anonymous
  • anonymous
very close! you halved it correctly, but there was something else you needed to do. Take another look at the final term of the last equation I gave you.
anonymous
  • anonymous
do i square it ?
anonymous
  • anonymous
yes! lol, so your equation becomes... y^2 + 4a + 4
anonymous
  • anonymous
o okay . thank you so much man
anonymous
  • anonymous
Yeah, np. lol. I bet you already figured out what the final form was by then working backwords... infact, if you know what you're doing, you can skip right to the final answer of \[(x+\frac{1}{2}a)^2\] ... which might have been what you did when you gave me your answer of 2... but I really suggest showing your work... teachers like to dock marks for skipping steps, lol

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