Question 747982
<pre>
f(x) = -x²-4x-7

Factor -1 out of the first two terms on the right.

f(x) = -1(x²+4x)-7

Complete the square inside the parentheses:

1. Multiply the coefficient of x by {{{1/2}}}.  4·{{{1/2}}} = 2
2. Then square that, get 4
3. Add then subtract 4 inside the parentheses. That
is, add +4-4 which does not affect anything since 
4-4 is just 0.  Also change the parentheses to 
brackets so they can hold parentheses:

f(x) = -1[x²+4x+4-4]-7

Group the first three terms inside the bracket in a 
parentheses:

f(x) = -1[(x²+4x+4)-4]-7

Factor that trinomial (x²+4x+4) as 
(x+2)(x+2) or (x+2)²

f(x) = -1[(x+2)²-4]-7

Next we remove the bracket by distributing the -1 
into the bracket.  The -1 first multiplies by the
(x+2)² leaving it intact as -1(x+2)².  Then the -1 
also multiplies by the -4 in the bracket and gives 
+4.  So we have this:

f(x) = -1(x+2)²+4-7

and finally:

f(x) = -1(x+2)²-3

Edwin</pre>