[ Music ]
>> All right, so we're
going to go ahead and get
into the second example here.
3x squared plus 10x minus 25.
And the directions are to solve
using the quadratic formula.
So you can see here
that a is equal to 3.
b is equal to 10, and c
is equal to negative 25.
So we're just going to
go ahead and plug all
that into the formula.
We get that x is equal
to negative 10 plus
or minus the square root of 10
squared minus 4, our a was 3
and our c was negative 25.
And this is going to be all
over 2 times a which was 3.
Okay, so then we get x is
equal to negative 10 plus
or minus square root
of 10 squared is 100.
Two negatives make a positive.
If you have four 25's you
have 100 and times 3 is 300.
This is all over 6.
We get x is equal
to negative 10 plus
or minus the square
root of 400 all over 6.
Now the square root of 400 is
like 4 times -- is that perfect?
Yeah, it's 20, right?
So x is equal to negative 10
plus or minus the square root
of 400 is perfect so
it's 20, all over 6.
So this is the point where you
could do the LCD if you want.
So let's go ahead and do that.
Get negative 10 over 6
plus or minus 20 over 6.
So we got x is equal to negative
10 over 6 is negative 5/3.
Plus or minus 20 over 6
that's like, is that 10/3.
Okay, so now you have to
account for the plus and minus.
So here's where we
get the two solutions.
So we got x is equal to
negative 5/3 plus the 10/3.
And then we also got x is equal
to negative 5/3 minus the 10/3.
And we already have an LCD.
So 10 minus 5 is 5.
And negative 5 minus
10 is negative 15.
And that still reduces.
I didn't know these
problems would be so long.
Okay, so then we get that x is
equal to 5/3, and we also get
that x is equal to this
will reduce to negative 5.
So these are the solutions
I got to this example.
All right, so here's
a third example.
Notice it's not in standard
form with zero on one side
and all the other stuff
on the other side.
So if it's not in standard form,
you want to just go ahead and do
that yourself already.
So let's get this
in standard form.
And I just want to mention
that you don't have to,
but it's better if
your leading term,
the coefficient is not negative.
So I wouldn't want to subtract
x squared over right now.
I would rather just move
all this stuff on that side,
so I'm working with a
positive leading coefficient.
So I'm run into less problems.
So let's add the 4x
and add the 1 over.
So then we get x squared
plus 4x plus 1 equals 0.
And now I can what
my a, b, and c are.
a is equal to 1.
b is equal to 4,
and c is equal to 1.
So let's plug it into that
formula and see what happens.
So you got x is equal
to negative b was 4 plus
or minus the square root
of 4 squared minus 4.
Our a was 1.
Our c was 1.
This is all over 2 times
a, which is 1 again.
So we get that x is
equal to negative 4 plus
or minus the square root
of 16 minus 4 all over 2.
So then we get x is
equal to negative 4 plus
or minus square root
of 12 over 2.
Now let's, square root of 12,
negative 4 plus or minus --
can be rewritten as 3 times 4.
And that 4's going
to pop out as a 2.
So then we get x is
equal to negative 4 plus
or minus 2 rad 3 all over 2.
And now we could split up
the LCD to get negative 4
over 2 plus or minus
2 rad 3 over 2.
So then we come over here.
And we got a plus
and a minus case.
So we have x is equal to, well,
negative 4 over 2
is just negative 2.
So I'm going to -- so this
comes down to negative 2, right?
So then you got negative 2 plus
that and negative 2 minus that.
So negative 2 plus
2 rad 3 over 2.
And then you got x is equal to
negative 2 minus 2 rad 3 over 2.
And notice these 2's just
slice off like butter.
So there goes that and that.
So our solutions that
we get are x is equal
to negative 2 plus
rad 3 and x is equal
to negative 2 minus rad 3.
So these are the
solutions that I got.
It's really not bad.
It's all just plugging in.
So just make sure you don't
make an algebra mistake.
All right, so I've
done a couple examples.
So why don't you guys go
ahead and give this a shot.
2x squared plus 8x
equals negative 3.
Solve using the quadratic
formula.
And then I'll go
over it with you.
So you need to have it
in standard form first.
Zero on one side, all the
other stuff on the other.
So I'm just going to add the 3
over as opposed to moving all
that stuff on the other side.
So I get 2x squared
plus 8x plus 3 equals 0.
So then I get that
a is equal to 2.
b is equal to 8.
And c is equal to 3.
So let's pop it in there.
x is equal to negative 8
plus or minus the square root
of 8 squared minus
4 -- what was our a?
2, and our c was 3.
And this is all over 2
times our a which was 2.
So then we get x is
equal to negative 8 plus
or minus the square root
of 64 minus 8 times
3 is 24 all over 4.
Then we get.
Negative 8 plus or
minus the square root
of that looks like 40.
Looks like 40.
So we're going to 40.
All right, so then
you come over here
and you got x is
equal to negative 8.
I know I'm not explaining
much in these videos
because it's just plug and chug.
So you got negative
8 plus or minus.
Now 40 again, some
guy hiding in there.
It's like 4 and 10.
All over 4.
So this is negative
8 plus or minus
that 4's going to
come out as a 2.
All right.
So here we have x is
equal to negative 8.
Now let's go ahead and split
up the LCD at this point.
Negative 8 over 4 plus
or minus 2 rad 10 over 4.
And then let's erase
all this stuff.
And let's get to work.
So this'll be 2, and this'll --
2 goes into 4 two times, right?
So look like that, right?
Negative 2.
So we got x is equal to
negative 2 plus and we also have
that x is equal to
negative 2 minus.
Of rad 10 over 2.
And you can't do much with this.
So notice that we got an
irrational solution here
because of the square root.
So that must meant that we
couldn't have actually factored
the original equation that
I had written here early.
So it wasn't a bad idea
to use the quadratic
formula on this one.
All right, so here's
another example.
So the first thing we're going
to do is get it in standard form
because we notice it's
not in standard form.
So I'm going to add this over,
as opposed to bringing
the other stuff over.
So then we get 2x squared
minus 3x minus 10 equals 0.
We can't divide to work
with smaller numbers.
So let's just seek out
what our a, b, and c are.
My a is 2.
My b is negative 3, and
my c is negative 10.
So we're going to take
all that and plug it
into this massive formula.
So then x is equal to
negative, my b is a negative,
so be careful with that.
Plus or minus the square root of
my b was a negative 3 squared.
It was a negative 3, but
I'm going to square it.
Minus 4. My a was like 2.
And my c was negative 10.
And this is all over 2
times my a, which was 2.
Okay, so then we just
simplify a little bit.
We get that x is equal to,
two negatives make a positive.
So then we get a 9 out of that.
Two negatives make a positive.
4 times 2 is 8, 8
times 10 is 80.
This is all over 4.
So then you get x
is equal to 3 plus
or minus the square root of 89.
It's just the square root of 89.
So then that's over 4.
And so we're going to account
for the plus and minus now.
So we get that x is equal to 3
plus square root of 89 over 4.
And we get that x is equal
to 3 minus the square
root of 89 all over 4.
In some cases, this
guy right here
in the denominator will
divide into this number
or if this square root has
a number in front of it,
so you'd want to
simplify further.
But in this case it
doesn't, so I'm going
to leave my answers like that.
