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#1 2006-12-28 04:50:53

Kiran
Member
Registered: 2006-11-15
Posts: 177

Equation solving wht next?

solve the following equation by completing the square:

9x^2 + 3x - 8 = 0

divide by 9
9/9 = 1
3/9 = 1/3
8/9 = 8/9
x^2 + (1/3)x - (8/9) = 0
add 8/9
x^2 + (1/3)x = (8/9)
(1/3)/2 = 1/6
(1/6)^2 = 1/36
add 1/36 both sides
x^2 + (1/3)x + (1/36) = (8/9) + (1/36)
( x + (1/6))^2 = (8/9) + (1/36)
(x + (1/6))^2 = (8/9) + (1/36) = 32/36 + 1/36 = 33/36 = 11/12
(x + (1/6))^2 = 11/12
x^2 + (1/6))^2 = 11/12
x^2 + 1/6^2 = 11/12
x^2 + 1/36 = 11/12
11/12 - 1/36 = 8/9
x^2 = 8/9


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#2 2006-12-28 05:51:05

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Equation solving wht next?

You made a mistake here:



  [Square root both sides]

LaTeX rocks!

Last edited by Toast (2006-12-28 05:57:21)

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#3 2006-12-28 05:59:54

slfer100
Member
Registered: 2006-09-11
Posts: 106

Re: Equation solving wht next?

ok i want to try try this y+2/x y =0,=5 ( it is easy)


naver give up on the war of love unless if you want to! big_smile

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#4 2006-12-28 06:05:39

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Equation solving wht next?

Sorry, what do you want to find?

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#5 2006-12-28 07:58:28

Kiran
Member
Registered: 2006-11-15
Posts: 177

Re: Equation solving wht next?

they need us to complete the square


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#6 2006-12-29 04:28:20

slfer100
Member
Registered: 2006-09-11
Posts: 106

Re: Equation solving wht next?

opps forgot to put in that qusiosn now i forgt.......


naver give up on the war of love unless if you want to! big_smile

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#7 2006-12-29 04:33:30

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Equation solving wht next?

uh, could you make it a bit clearer? I don't really understand the equation.

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#8 2006-12-29 06:49:15

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Equation solving wht next?


Solution:


Solution:
x=-2 : y elem R
x!=0,-2 : y=0


Solution:
x!=0,-2:

Last edited by krassi_holmz (2006-12-29 06:49:47)


IPBLE:  Increasing Performance By Lowering Expectations.

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#9 2006-12-29 10:30:34

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,697

Re: Equation solving wht next?

For reference: Completing the Square


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2007-01-02 03:34:39

Kiran
Member
Registered: 2006-11-15
Posts: 177

Re: Equation solving wht next?

soooooooo by using the reference i did:
9x^2 + 3x - 8 = 0
x^2 + 3/9x - 8/9 = 0
x^2 + 3/9x = 8/9
x^2 + 3/9x + (3/81)^2 = 8/9 + (3/81)^2
(x + 3/81)^2 = 8/9 + (3/81)^2
(x + 1/27)^2= 8/9 + 9/6561 = 649/729
(x + 1/27)^2 - 649/729 = 0
27(x + 1/27)^2 - 649/729 = 0
27(x + 1/27)^2 = 649/27
(x + 1/27)^2 = 649/729
x + 1/27 = +- sqrt(649/729)
x = 1/27 +- sqrt(649/729)
x = -703.5 ... and -0.906....

correct


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#11 2007-01-02 04:13:32

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Equation solving wht next?

Starting at line 3 of the above: 3/9 = 1/3, so we can write:
x^2+1/3x=8/9

BUT... x^2 + 3/9x + (3/81)^2 != (x+3/81)^2   !

the formula is (a+b)^2 = a^2 + 2ab + b^2
a is x, so the coefficient before x sould be 2b:
1/3 = 2 b
b = 1/6
so not (3/81)^2, it must be (1/6)^2.

...and the ansers are:


IPBLE:  Increasing Performance By Lowering Expectations.

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