# Solve for x

#### Amer

##### Active member
Solve for $x$:

$$4x^2 +4xy - 6y - 9 = 9$$

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#### MarkFL

Staff member
I would write the equation as a quadratic in x in standard form:

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

#### Amer

##### Active member
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

Staff member
What happened to the 9 originally on the right side?

#### MarkFL

Staff member
I've made a few of those in my time!

#### CaptainBlack

##### Well-known member
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
Last line should be:

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

CB
what is wrong in my solution ?

#### earboth

##### Active member
Solve for x:

$$4x^2 +4xy - 6y - 9 = 9$$
what is wrong in my solution ?
Since x is the variable and y is considered to be a constant your solution should read

$$|2x+y| = y+3$$

as CB has pointed out.

#### freiermuthj

##### New member
Or you can use POLYSMLT if you have a TI83