Question

Completing square

Answer 1

Where's the equation?

Answer 2

\[75+\frac{ 100i }{ n }-\frac{ 100i^2 }{ n^2 }\]

Answer 3

just for simplicity, treat i/n = x
so we have
-100x^2 +100x +75
right ?

Answer 4

we need to have the co-efficient of x^2 as 1
so start by factoring -100 out
\(-100 (x^2-........?)\)

Answer 5

actually i have to turn this form\[\frac{ 10 }{ n }\sqrt{75+\frac{ 100i }{ n }-\frac{ 100i }{ n^2 }} -->\frac{ 10 }{ n }\sqrt{100-(-5+\frac{ 10i }{ n })^2}\]

Answer 6

yes. we will get there onlt

Answer 7

only

Answer 8

ya how do i do that? can u help me step by step?

Answer 9

so start by factoring -100 out
−100(x^2−........?)

Answer 10

you got the step where i took, i/n = x, right ?

Answer 11

-100(x^2-x-75/100)

Answer 12

yup!, after tht?

Answer 13

now divide the co-efficient of 'x' by 2

Answer 14

you mean the one outside the bracket?

Answer 15

ok, whats the co-efficient of x, first tell that
in ax^2+bx+c, the co-efficient of x is b

Answer 16

ah okay haha, -1?

Answer 17

yes, so dividing it by 2 gives -1/2
now square it, what u get ?

Answer 18

1/4x^2?

Answer 19

actually there are standard steps to complete the square, we add and subtract,
\((co-efficient ~of ~x /2)^2\)

Answer 20

where did x^2 come from ?
square of -1/2 is just 1/4

Answer 21

a co-efficient is a constant multiplied with x

Answer 22

oh okay, i thought x also haha, okay thenit is -100(x^2-1/4x-0.75)

Answer 23

so we add and subtract 1/4
keep 0.75 as 3/4

-100 \((x^2 -x +1/4 -3/4 -1/4)\)

got this ? i just added and subtracted 1/4 in what u previously had

Answer 24

oh so u mean the x and its coefficient are not in one term? i see, it make sense since coefficient would still be 1

Answer 25

then afterwards?

Answer 26

yes, we cannot change the expression, it was x^2 -x -3/4 before,
it must be that afterwards too (notice that adding and subtracting 1/4 will not chnage the expression)

and then do you notice a perfect square trinomial ?
x^2 - x +1/4 = (..??.. )^2

Answer 27

like for example x^2 +2x+1 = (x+1)^2
\(x^2-x+1/4 = (x-what?)^2\)

Answer 28

uhm.. what is it haha, im kinda bothered with the 1/4 there

Answer 29

2 ways to find out,
1) see the last term, constant, 1/4
its like (a+b)^2 = a^2+2ab+b^2, the last term b^2 is the square of 'b'
so here. we'll have square of ... ?

2) that "what?" term is same as the answer you got before squaring in the 2nd step

Answer 30

hm so (x-1/2)^2, sorry my head is abit laggy now haha

Answer 31

thats correct :)
we have
\(-100((x-1/2)^2 -1)\)
right ?
now just distribute the -100 inside

Answer 32

100(x-1/2)^2+100

Answer 33

-100 (x-1/2)^2 +100

Answer 34

oh ya haha then?

Answer 35

now 100 is 10^2 , so when it goes inside a square term,
\(100 - [10(x-1/2)]^2\)
got this ?

Answer 36

i missed a step,
100 - 10^2 (x-1/2)^2
100- [10 (x-1/2)]^2

Answer 37

okay got it then after?

Answer 38

whats 10 (x-1/2) = ... ?
simplify

Answer 39

10x-5

Answer 40

and x = i/n

Answer 41

ahh! okay i see wow, nice! haha xD thank u very much! (:

Answer 42

you're welcome ^_^

Answer 43

did u draw that? emelove

Answer 44

draw what? @dan815

Answer 45

ur picture

Answer 46

oh, nah haha i put my face in an iphone app called moment cam haha, it shd be quite popular.. why do alot of people ask me, oh well.. haha

Answer 47

oh okay no wonder

Answer 48

cuz i was gonna say the eyes look crazy

Answer 49

like professional

Answer 50

looks can be deceiving.. :p u can try to dl it if u have iphone and see for urslf (: