Use the method of completing the square to transform the quadratic equation into the equation form (x – p)2 = q. 12 - 8x2 + x4 = 0

First things first.  We have to get that into standard form.  is what I'm seeing.  Hope I did not misinterpret.  In order to complete the square, we need to do 2 things.  First let's set the quadratic equal to 0, then move over the 12 by subtraction.  .  The rule for completing the square is that the leading coefficient HAS to be a +1.  Ours is a -8, so we have to factor it out.  When we do that, we will get .  Now we are ready to complete the square.  Take half the linear term, square it, and add it to both sides.  Our linear term is 1/2.  1/2 divided by 2 is 1/4.  If we square 1/4 we get 1/16.  So we add it in.  HOWEVER, we have that -8 hanging around out front on the left, refusing to be ignored.  If we add in 1/16 into the parenthesis, we have to multiply it by -8 and add whatever that product is onto the right side.  -8*1/16= -1/2.  This is what all that looks like: .  In this process we have created a perfect square binomial on the left, which is this: .  If I'm not mistaken, that's the form you need it in.