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Solve for x

Amer

Active member
Mar 1, 2012
275
Solve for $x$:

$$4x^2 +4xy - 6y - 9 = 9 $$
 
Last edited by a moderator:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I would write the equation as a quadratic in x in standard form:

$\displaystyle 4x^2+4yx-(6(y+3))=0$

Now apply the quadratic formula.
 

Amer

Active member
Mar 1, 2012
275
Completing the square

$ (2x)^2 + 2(2x)y -6y - 9 = 0 $
$ (2x+y)^2 -y^2 -6y - 9 = 0 $
$(2x+y)^2 - (y+3)^2 = 0 $
$(2x+y)^2 = (y+3)^2 $
$ 2x+y = |y+3| $
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
What happened to the 9 originally on the right side?
 

Amer

Active member
Mar 1, 2012
275

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I've made a few of those in my time! (Tauri)
 

CaptainBlack

Well-known member
Jan 26, 2012
890
Completing the square

$ (2x)^2 + 2(2x)y -6y - 9 = 0 $
$ (2x+y)^2 -y^2 -6y - 9 = 0 $
$(2x+y)^2 - (y+3)^2 = 0 $
$(2x+y)^2 = (y+3)^2 $
$ 2x+y = |y+3| $
Last line should be:

\(2x+y = \pm(y+3)\)

CB
 

Amer

Active member
Mar 1, 2012
275

earboth

Active member
Jan 30, 2012
74

freiermuthj

New member
Oct 11, 2012
1
Or you can use POLYSMLT if you have a TI83