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- anonymous

How do you complete the square?

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- anonymous

How do you complete the square?

- katieb

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- anonymous

with lines

- anonymous

I mean with like quadratic equations...

- anonymous

u add square of half the coefficient of x to both sides.....

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- anonymous

if u give a question I can explain..

- anonymous

Got it!

- anonymous

good for u then....☺

- 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

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

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

it will give you C = 25.
Thats the number you were looking for ;)

- anonymous

I've found this out by myself when i was in college. It was very useful for my advanced math classes

- anonymous

I've found this out by myself when i was in college. It was very useful for my advanced math classes

- anonymous

25 = 5² which is square of half of the coefficient of x as I said !!!

- anonymous

well.. here is the proof of what you said then.
only words doesnt mean anything :p

- anonymous

could I have another example?

- anonymous

Just to get it in my brain :)

- amistre64

abstract: ax^2 +bx +c
c = (b/2)^2

- anonymous

x^2 + 4x + C
4x = 2x*sqrt(C)
2 = sqrt(C)
C = 4
so: x^2 + 4x + 4 = perfect square

- amistre64

thats if a=1 i believe

- anonymous

thnx!

- anonymous

Thanks guys!

- amistre64

no prob

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