Question 22
<pre><font face = "courier new">This is a basic question but I can seem to explain it.
The Quadratic Equation term "b^2 -4ab" why do we change 
it to "b^2+ 4ab" when the "b" value is negative?
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We don't. First of all it's not b²-4a<b><font size = 4>b</font></b>, it's b²-4a<b><font size = 4>c</font></b>. 
Also your example:
b^2-4ab (x^2-6x-27=0) = 6^2+4(1)(-27)=144 
is incorrect in the next to last step, although 144 is correct.
It should be
b^2-4ab (x^2-6x-27=0) = 6^2<b><font size = 4>-</font></b>4(1)(-27)=144 
What you have there, namely,
6^2<b><font size = 4>+</font></b>4(1)(-27)=
equals to -72, not 144.

Suppose we have
     2x² + 5x - 3
then a=2, b=5, and c=-3
So
     b² - 4ac
becomes
     (5)² - 4(2)(-3)
or
     25 - (-24)
and then the " - " sign before the parentheses and the " - "  
before the 24 inside the parentheses becomes a " + ", and we
have
    25 + 24
or
    49 

Edwin