[ Intro Music ]
>> So why don't you just
go ahead and try this one.
X squared plus 36 equals
negative 12X, and the solution
to solve it using the
quadratic formula [inaudible].
So give it a shot, and then I
will go over it with you, maybe.
So you want to get
it in standard form
to get zero on one side.
So move the 12X rather
than all this stuff.
Because I want a
positive coefficient.
So I get X squared plus
12X plus 36 equals zero.
So that then I see
that A is equal to 1.
B is equal to 12.
And C is equal to 36.
So then you come over
here and plug it in.
Just plug in and
see what happens.
You get X is equal to negative
12 plus or minus of square root
of 12 squared minus 4AC.
12 over 2A.
So then you get that X is
equal to negative 12 plus
over minus the square root of
144, that's what 12 squared is.
4 times 36 is also 144.
And this all over 2.
This 144 minus 144 is
zero, so it goes away.
Then we get negative 12 plus or
minus zero all over 2, right.
So now we can split
up the LCD if we want.
So we get negative 12 over
2 plus or minus zero over 2,
then we get X is equal to
negative 12 over 2 plus
or minus zero divided
by 2 is zero.
So all this stuff goes away,
now we're just left with this.
And we get that X is
equal to negative 6.
So notice we've only got
one solution this time.
So that means that if we
wanted to do this example prior
and did the discriminate,
we would have saw
that D equals zero.
Which we saw here.
So we only get one solution.
Okay, so I'm going to go
ahead and do this one.
So let's just jump
right into it.
We've seen the case where
we've got two solutions.
We saw the case where
we had one solution.
So this is probably
going to be imaginary,
hence, hence, wink wink.
So let's go ahead and do it.
So we've got A is equal to 3.
B is equal to 4.
And C is equal to 5.
Plug that into this crazy thing.
X is equal to negative B was
4 plus or minus square root
of 4 squared minus
4A or C was what, 5.
And this is all over 2
times A, which was 3.
Then we come over here
and we get negative 4 plus
or minus the square
root of 16 minus this is
like 12 times 5 is 60.
All over 6, you get negative 4
plus or minus the square root.
So you got 16 minus 60,
that's a negative 44.
Notice I said negative,
and it's under the radical.
So what could that mean?
So we got negative
4 plus or minus.
First of all, we have to rewrite
that as 4 times 11
negative 4 times 11,
okay, and that's over 6.
So it's going to come
out as a negative 4.
It's going to come out of
the 2I, because, you know.
Then you get negative 4 plus
or minus 2I rad 11 over 6.
Now we're going to
split up the LCD.
The reason it came
out as an I is
because when you have a negative
under the radical,
it comes out as an I.
So then you get negative
4 over 6 plus
or minus 2I rad 11 over 6.
So here we go.
You got X is equal to -- because
our focus is on this now, right.
So negative 4, 6
is negative 2/3.
So we've got negative
2/3 plus something.
And we got negative
2/3 minus something.
And then notice that the 2
and the 6 you just
get a 3 on the bottom.
So you get rad 11 I over 3 and
then you get rad 11 I over 3.
Okay, so that was
the imaginary case.
They do have the same
LCD, so we could write it
as a single fraction, which is
probably what the professors
would like.
So let me just go
ahead and do that.
So our final answer
would be X is equal
to negative 2 plus rad 11
I over the LCD which was 3.
And then the other
answer was the same thing
but with a minus, right.
So negative 2 minus
rad 11 I over 3.
So this is a better
way, I guess.
If you can go further,
this would be it.
But you can give it a
shot and I'll go over it.
Just notice that there's no 3
terms here, so the B is missing.
So B is zero.
So A equals 1.
B equals zero because
it's missing.
And C is equal to 25.
And let's see what happens.
So we get X is equal to
negative B which is zero plus
or minus the square
root of B squared,
so zero squared minus 4.
Our A was equal to 1.
And our C was 25.
This is all over 2 times
A, and our A was 1.
Then you get X is equal
to zero, it goes away.
Plus or minus square root
of zero goes away again.
The negative remains.
4 times 25, you have 4 quarters,
you have a dollar,
I don't know, 100.
I just think in a weird way.
So then that's over 2.
This is equal to plus or minus.
That negative comes out as an I.
And the square root
of 100 is 10.
And it's over 2.
And this and that.
Okay, so 10 goes into 2 5 times.
So you get plus or minus 5 I.
Then you get X is equal to 5 I
and X is equal to negative 5 I.
Okay, so you know, when we
look at our answers usually,
we're like, could we
have factored that
or what could we
have done and looking
at the discriminant or what not.
But looking at this, the easiest
way to go about doing this is
to go about the square root
property or the extracting
of roots, because we can
isolate the square quantity
or variable in this case.
And so if you haven't seen
that, I did a video on that
on the square root properties,
so you can check that out.
So this doesn't even look
quadratic in the first place.
It's not an easy
quadratic formula.
So why don't we distribute
this negative X
into this parenthesis
and see what happens.
So let's pop that in there.
So we get a 5X minus a
2X squared equals a 7.
So now we've got
a second degree.
It's looking quadratic, cool.
I don't really want my
leading term, the coefficient
on my leading term
to be negative,
so why don't we just move
all this stuff to that side.
Add the 2X over, so you get
2X squared minus the 5X over.
And the 7 was already
there, okay.
So this is looking nice.
So my A is equal to 2.
My B is equal to negative 5.
And my C is equal to 7.
Let's pop them in here
into the quadratic formula.
So we get X is equal
to negative.
My B was negative 5 plus
or minus the square root
of my B was negative 5.
We're going to square
that minus 4.
My A was 2.
And my C was 7.
And this is all over 2
times my A which was 2.
Okay, so now two negatives
make a positive, that's 25.
That's a negative.
So then here you get 2 times
4 is 8 and 8 times 7 is 56.
And this is all over 4.
So then we get that
X is equal to 5 plus
or minus the square root
of that looks like 31
or something ugly,
like negative 31.
It's ugly.
So then that's all over 4.
All right, so you know what
the negative do, right?
I's come up or imagineries,
because you can't have
negatives under the radical.
And you know, if you did the
discriminate on this and got
that D was less than zero, you
would have saw that earlier.
All right, so you got X is equal
to 5 plus there's the rad 31,
because there's nothing
you can do with that.
But that negatives
comes out as an I.
This is all over 4.
Then you get that
X is equal to 5
with minus now the square
root of 31 I all over 4.
So these two were
the solution, okay.
So it's come to that time of day
where it's the last
problem of the day.
So why don't you go
ahead and give it a try,
and then I'll go
over it with you.
Okay, so again, this
doesn't even look quadratic.
It's not even in our mindset
that we're looking for.
We want it to be
quadratic second degree.
So let's pop this
thing with 3X in there.
So then we get like a
negative 3X squared.
Two negatives is positive.
6X equals 5.
And I want to get it in extended
form, but like my leading terms,
I have a positive coefficient.
So let's move all
this to that side.
So you add the 3X over.
You add the negative
3X square over.
You subtract the 6X over.
And the 5 was already here,
so we can't kick him out.
Now we just see [inaudible]
A, B, and C are.
So A is equal to 3.
B is equal to negative 6.
And C is equal to 5.
Plugging it into here, we get
that X is equal to negative.
My B was negative, so
be careful with that.
Plus or minus the square
root of my B squared minus 4.
My A was 3.
And my C was 5.
And this is all over 2
times my A which was 3.
Okay, so now we just simplify.
So we get X is equal to,
two negatives is positive,
plus or minus the square root of
that's a 36, that's a negative.
Let's see here, that's
a 12 times 5 is 60.
That's all over 6.
So then you get X is equal to 6
plus or minus 6 square root of.
Well, I would need 4 to get
to 40 and 20, so negative 24.
So you get negative 24.
All right, that negative
has to come out as an I
and that 24 is trying
to sneak something in,
like a 4, 4 times 6.
So we're going to
take that 4 out.
Square root of negative
4 times 6 all over 6.
All right, that negative 4 is
going to come out as a 2 I.
So then we get that
X is equal to 6 plus
or minus 2 I square
root of 6 all over 6.
This is the case where this
denominator number goes
into that number and the 2.
We're going to split up and get
that X is equal to 6 over 6 plus
or minus 2 I square root
of 6 over 6 so then we get
that X is equal to
this would be a 1 plus
or minus that would be 3.
So we get square
root of 6 I over 3.
I guess that looks better.
So thank you.
That was it for the
quadratic formula.
I'm sure you'll never
forget that formula.
So I'll see you next time.
