Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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

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

Live 4 Love

Offline

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

You made a mistake here:

[Square root both sides]

LaTeX rocks!

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

Offline

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

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!

Offline

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

Sorry, what do you want to find?

Offline

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

they need us to complete the square

Live 4 Love

Offline

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

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

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

Offline

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

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

Offline

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

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.

Offline

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

For reference: Completing the Square

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

Offline

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

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

Live 4 Love

Offline

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

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.

Offline

Pages: **1**