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#1 2006-12-28 04:50:53
- Kiran
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- Registered: 2006-11-15
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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
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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
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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! 
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#4 2006-12-28 06:05:39
- Toast
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Re: Equation solving wht next?
Sorry, what do you want to find?
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#5 2006-12-28 07:58:28
- Kiran
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Re: Equation solving wht next?
they need us to complete the square
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#6 2006-12-29 04:28:20
- slfer100
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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!
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#7 2006-12-29 04:33:30
- Toast
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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
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- Registered: 2005-12-02
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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
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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
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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
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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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