People often use the Quadratic Formula
in
inappropriate situations.  First, the
statement of the Quadratic Formula is
if a x square plus b x plus c equals 0
then, this says you can't use this thing
unless you have a quadratic equation, so
in this situation x square minus 5 x plus one
this isn't even an equation.  Yes, it's
quadratic
but you can't solve for x at all,
never mind with the Quadratic Formula.
So in general you can't solve algebraic
expressions for x.
Here's another example:  x square minus 3 x
equals 6. Yes, this is an equation.  Yes, this
is a quadratic equation,
but it's not in the right form.  You have to
have a x squared plus b x plus c
equals 0.  The 0 has to be all by itself
on the right,
all terms have to be pushed to the left,
all terms have to be in the right order,
Easily, this guy's easy to fix.  If you
subtract 6 from both sides,
boom.  He's in the right form you're good
to go, and so
a equals 1, b equals -3, and c equals -6,
And here you go: all three numbers put in
the right spots
all the reductions done, so this guy is
simplified as much as he possibly can be
there are two different roots and they're
both
real.  Finally what about this quadratic
equation?
It's in the right form: a equals one, b equals five, c equals 6.
I hear folks say "No you shouldn't use the
quadratic formula
because you can factor this." No, it's
true that you can factor
but the quadratic formula works
perfectly well.
Check it out: you put all the numbers
where they're supposed to go and you reduce.
and you get two beautiful whole number roots, -2 and -3.
You don't have to use the Quadratic
Formula; check how easy it is once you
factor this quadratic equation, you get
the same two roots.
But what I'm trying to say is the
quadratic formula works
all time for every quadratic equation
whether it factors or not.
