Question

How do you complete the square?

Answer 1

with lines

Answer 2

I mean with like quadratic equations...

Answer 3

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

Answer 4

if u give a question I can explain..

Answer 5

Got it!

Answer 6

good for u then....☺

Answer 7

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

Answer 8

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

Answer 9

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) )

Answer 10

it will give you C = 25.

Thats the number you were looking for ;)

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

could I have another example?

Answer 16

Just to get it in my brain :)

Answer 17

abstract: ax^2 +bx +c

c = (b/2)^2

Answer 18

x^2 + 4x + C

4x = 2x*sqrt(C)
2 = sqrt(C)
C = 4

so: x^2 + 4x + 4 = perfect square

Answer 19

thats if a=1 i believe

Answer 20

thnx!

Answer 21

Thanks guys!

Answer 22

no prob