This video is going to be about the quadratic formula. And the quadratic formula is a formula
you can use
if you've got a quadratic equation
and you can't solve it by any 
of the other methods you know.
So let's look at an example.
Here I've got the equation 
2x squared minus 3x minus 9
equals x squared.
So the first thing we do
if we want to solve this
is
get all of the terms on
one side of the equation.
So I'm going to subtract x squared
from both sides
and that leaves me with
x squared
minus
3x
minus 9
equals 0.
Now, you could try to solve this... 
Actually, let's do that.
Let's see if we can solve this 
one of the ways we know.
So since I've got an x-squared, 
I'll put an x here and an x here.
I know I've got a negative sign 
over here for my third term,
so I'm looking for two factors of 9,
one positive and one negative,
And when I add them together, 
I want to get a negative 8.
Well, the only way I can factor 9 
would be 1 times 9
and the difference between 1and 9 
is not negative 3,
or 3. And the other way would be
negative 3 times positive 3,
but
the sum of negative 3 
and positive 3 is 0.
So that's not gonna work.
So it seems like 
I can't factor this.
But, like I said, 
you can
always use the quadratic formula
and that will solve things.
So here's the way we do it...
First we make sure the equation is in 
what's called standard form. Standard form
means
your exponents
are in descending order.
I've got an x squared
and then x to the first 
and then I've just got a constant,
and
all my terms are on 
one side of the equation
and I've got a zero 
on the other side.
The next thing to do is look at your
coefficients. Well I've got this x squared,
which means the coefficient is 1.
And now we're going to assign a
letter to each coefficient. In other words,
I'm going to say that 
the first coefficient, the 1
is my 'a',
and negative 3
is my 'b',
and negative 9 is my 'c'. I'll write those 
over here. So, a equals 1,
b
equals
negative 3
and c equals
negative 9.
Now we're gonna write 
the quadratic formula
which
you want to make sure 
you've got memorized.
So the quadratic formula is x
equals
negative b
plus or minus
the square root
of
b squared
minus 4
a
c
and that's
over
to a.
And now what 
we're going to do
is
take these values, 
the a, b and c values
and plug them in where I have 
an a or a b or a c in the quadratic formula.
So I'll get
x equals
negative...
b is negative 3,
negative negative 3
plus or minus
the square root
of 
negative 3
squared
minus 4
times a, 
which is 1
times c,
which is
negative 9,
and that's all going to be divided
by
2
a, and a is 1.
And now the only this 
left to do
is just do the math for all of this. 
Oh, I'm sorry,
I wanted a 3 here.
So here we go.
x equals
negative negative 3,
it's a positive 3,
plus or minus
the square root
of...
negative 3 squared is 9...
minus 4 times 1... 
Minus 4 times 1 is negative 4,
negative 4 times negative 9 
is positive 36,
and this is 
going to be over
2. Now, before I run out of room
I'll continue over here.
This next step is I want to 
combine this 9 and 36.
So now I've got that x equals
3
plus or minus...
9 plus 36 is 45
and
that's over 2.
And now I've just 
got to factor...
I've got to simplify the 45. 
45 is not a perfect square
but 45 is 9 times 5,
and 9 is a perfect square.
So
x equals 3
plus or minus
the square root 
of 9 times 5
over 2.
Taking the square root 
of 9, that's 3.
So x equals plus or minus
3
times the square root of 5
over 2.
So this is my solution to 
that original equation.
Let me go back over the steps.
Take the original equation.
We put it into standard form, which
means we're going to get all of the
terms
on the left side, or on one side of the
equation, it doesn't matter which side,
and the other side of 
the equation will equal 0.
Then write down 
the quadratic formula.
Make sure you've got it memorized.
We take
each of the coefficients
and the first coefficient, 
the x-squared coefficient,
we call that 'a',
the x coefficient we call 'b',
and
the constant is called 'c'.
So we've got an 'a', a 'b' and a 'c',
and we've got the quadratic formula.
And now all you have to do
is plug the values that you've got, 
the a-, b-, and c-values
into the quadratic formula,
and then
do all the math,
and
here we are,
you're going to get a solution.
So none of the individual steps is hard 
in this. This is true of a lot of math.
Basically,
this process is made up
of a bunch of very simple steps,
but you've got to have the process
memorized and you've got to be very
careful as you go through to each step
not to make a careless mistake. 
I want to do another example, but 
there's not going to be time in this video,
so I'll come back with another one.
See you soon.
