anonymous
  • anonymous
How do you complete the square?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
with lines
anonymous
  • anonymous
I mean with like quadratic equations...
anonymous
  • anonymous
u add square of half the coefficient of x to both sides.....

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anonymous
  • anonymous
if u give a question I can explain..
anonymous
  • anonymous
Got it!
anonymous
  • anonymous
good for u then....☺
amistre64
  • amistre64
in algebra we are given an equation; quadratic in nature usually; and in order to "complete the square" we can look to geometry: for instance: x^2 +6x + ??? completes the square set it up like this \begin{array}c &&&6/2\ xs\\ &x^2&x&x&x\\ &x&1&2&3\\ 6/2\ xs&x&4&5&6\\ &x&7&8&9\\ \end{array} it take an additional 9 pieces to "complete" the square
amistre64
  • amistre64
while the geometry is useful to describe what a "complete square" square is; it impractical to use all the time; so we take our lead from it and abstractly construct our square with half of our "x" coefficient; and square it
anonymous
  • anonymous
example: you have x^2 + 10x + C you want to find C. just simply solve this equation: \[10x = 2x*\sqrt{C}\] i mean, you have to match the second term with this expression ( 2x*sqrt(C) )
anonymous
  • anonymous
it will give you C = 25. Thats the number you were looking for ;)
anonymous
  • anonymous
I've found this out by myself when i was in college. It was very useful for my advanced math classes
anonymous
  • anonymous
I've found this out by myself when i was in college. It was very useful for my advanced math classes
anonymous
  • anonymous
25 = 5² which is square of half of the coefficient of x as I said !!!
anonymous
  • anonymous
well.. here is the proof of what you said then. only words doesnt mean anything :p
anonymous
  • anonymous
could I have another example?
anonymous
  • anonymous
Just to get it in my brain :)
amistre64
  • amistre64
abstract: ax^2 +bx +c c = (b/2)^2
anonymous
  • anonymous
x^2 + 4x + C 4x = 2x*sqrt(C) 2 = sqrt(C) C = 4 so: x^2 + 4x + 4 = perfect square
amistre64
  • amistre64
thats if a=1 i believe
anonymous
  • anonymous
thnx!
anonymous
  • anonymous
Thanks guys!
amistre64
  • amistre64
no prob

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