 
Hello.
Professor Poyser here again, and
I want to show you how to
use the quadratic formula to
solve this quadratic equation.
And once again, it is an
equation because of the equal
sign, and it's quadratic
because the largest
exponent is a 2.
I've got the quadratic
formula over here--
negative b plus or minus the
square root of b squared minus
4ac all over 2a.
So the first thing I'm going
to do to this equation-- in
fact, I'm going to show you two
different ways to solve
this equation.
Let's do it, though, first with
the quadratic formula
since that's what this question
is asking for.
But the first I'm going to do
here is I'm going to bring
that 9x that's on the right-hand
side over to the
left-hand side, along with
that 4x squared.
So now my equation
looks like this--
4x squared minus 9x equals 0.
I need to pick off what a, b,
and c are because that's
what's needed in my
formula over there
for the quad formula.
So I need to know what a is.
That's just the coefficient 4,
and b is that coefficient of
negative 9.
And I notice that there is no
constant term over here on the
left-hand side.
So since there is no constant
term, then that c must be 0.
So we've got all the players
now, and we're just going to
plug them into our quadratic
formula.
So here it goes.
I've got x is equal to--
and the way I read that ,
instead of reading it as
negative b, I often read that as
give me the opposite of b.
So since my b is a negative 9,
the opposite of that would be
a positive 9.
So I've got positive 9 plus or
minus the square root of b
squared-- so that's negative 9
times itself, which is 81--
minus 4 times a couple
of numbers.
This is interesting because
those numbers are 4, which is
my a, and 0, which is my c.
That's going to pose something
fun there.
We're going to come back
to that in a second.
All over 2 times a--
well, my a is a 4--
so it's 2 times 4.
OK.
So far, so good.
I hope you see that my
denominator is just simply
going to be an 8 because
2 times 4 is 8.
There's my denominator of 8.
I also have this 9 out front,
so it's 9 plus or minus.
But let's take a look a little
bit more closely at what's
happening inside of
this square root.
Now keep in mind that if all
of this stuff inside the
square root shrinks down to be
a negative number, then you
can stop right there because the
square root of a negative
number is not real.
We don't have to solve that,
at least not for Mat 099.
So, let's start with this.
Look, I've got some
multiplication to do over here.
And I hope you see that 0 times
either of these numbers--
times that 4, times that
4-- is just going
to give me a 0 anyways.
So I really have 81 minus 0.
And 81 minus 0, because all of
this stuff cancels out, 81
minus 0 is just 81.
So I have the square
root of 81 up top.
Well, we can simplify that
even a little bit more.
That just shrinks down to be a
9, plus or minus 9, because,
again, the square root of 81 is
just becoming that 9 right
there, all over 8.
Do you see that there
are two things
going on in this problem?
There's, up top in the
numerator, there's 9 plus 9
divided by 8.
And there's 9 minus
9 all over 8.
So there are two operations
going on.
Let me just slide this
up so you can see it
a little bit better.
There are two operations
going on up top here.
There's the plus, and there's
also the minus.
And I have to take both of those
into consideration, the
plus and the minus.
So for this first fraction,
9 plus 9.
Well, my numerator then becomes
an 18 all over 8.
And that simplifies down to--
hey, that's just, cut each
of those in half,
you get 9 over 4.
There's one answer showing up.
And the other one is a funny
case where 9 minus 9.
Well, that's just a 0.
So since that's just a 0 over
8-- well, 0 divided by any
number here really is just
going to give me a 0.
So my final other answer is 0.
It's coming from there.
So I have two answers
out of this.
I've got 9/4, and I have 0.
And that's exactly--
if you're using MyMathLab--
what you're going to type
in on MyMathLab.
It doesn't matter which number
you type in first.
So in the box in MyMathLab, you
can type in 0 comma 9/4.
And there is your final
answer for MyMathLab.
You can type the 9/4
first if you want.
Hope that helps.
 
