9y^2+18y=x^2+6x+9

Question

change this equation in standard form by completing the square. 

Answer 1

Step 1: 9*(y^2 + 2y    )  = x^2 + 6x + 9        <--- factors out 9 from the left side

 

 

Step 2:

9*(y^2 + 2y + 1) - 9  = x^2 + 6x + 9           <--- completes the square

 

Completing the square:

    take half of the coefficient of the linear term, then square that.

    The coefficient of the linear term is 2 as highlighted in bold in step 1.

     Half of that is one, and one squared is one. 

 

  So adding one on the inside of the parenthesis means that, by distributive property,

  1x9 = 9 is added to the left side. In order to compensate for that, it is required

   to subtract 9 from only the left side.

 

Step 3: 

 

if you want it multiplied out (standard form)

 

 9 y^2 + 18 y  =  x^2 + 6x + 9

 

or Factor as you wish

9 ( y + 1)^2 - 9 = (x + 3)^2