Question 1123174
<pre>The quadratic portion of 

{{{1/64 - 12x - x^2}}}

is just the 2nd and 3rd terms, so
we just work on those and pay no attention
to the {{{1/64}}} since it is not part of the
quadratic portion:

Write the 2nd and 3rd terms preceded by a - :

{{{1/64 - (-12x + x^2)}}}

Swap the terms in the parentheses to get 
the x² term first:

{{{1/64 - (x^2-12x)}}}

Take half of -12, getting -6,
Then square -6, getting (-6)² or 36, then
Add and subtract 36 inside the parentheses

{{{1/64 - (x^2-12x+36-36)}}}

Factor the first three terms inside the parentheses:

{{{1/64 - ((x-6)^2-36)}}}

Write the 36 as 6²

{{{1/64 - ((x-6)^2-6^2)}}}

Since that is the negative of the difference of two
squares, that may not be acceptible as the difference
of two squares.  In that case we distribute the -
to remove the outer parentheses:

{{{1/64 - (x-6)^2+6^2)}}}

The quadratic part is the sum of a negative square
and a positive square, so to make the quadratic
part into the difference of two squares, we reverse
the 2nd and 3rd term so that it will
be the difference of two squares:

{{{1/64 + 6^2 - (x-6)^2)}}}

Now the 2nd and 3rd terms (the quadratic portion)
are the difference of two squares.

Edwin</pre>