This is going to the second video 
about using the quadratic formula.
So here's an example.
I've got x plus 1 equals 
2x squared,
and
I want to use the quadratic 
formula to solve this.
So I want to put it 
into standard form.
And here's a point 
I want to make...
I could subtract 2x squared from 
both sides and get everything,
all of my terms over 
on the left side,
but maybe I don't want to 
start with a negative 2.
So
I could also subtract x and 1
from this side, from the left side,
and get all my terms 
over here.
So the left side is 
going to equal 0
and the right side 
is going to be
2x squared
minus x minus 1.
In other words, 
it doesn't matter
which side to get all 
of your terms on,
because if I have 0 equals 
2x squared minus x minus 1,
that's the same as saying
2x squared minus x minus 1
equals 0.
So I just wanted 
to make that point.
Now,
this equation is 
in standard form,
and
and I'm going to 
figure out what my a, b, and c
values are.
Well, 'a'
is the coefficient of the squared term, 
the x squared over here,
so 'a' is going to equal 2.
'b' is the coefficient 
for the...
x-to-the-first term, 
the middle term,
and since there's no coefficient 
written it's just going to be
in this case, 
a negatively 1.
and 'c'
is also negative 1.
So now I'm going to write 
my quadratic formula.
That's x equals
negative b
plus or minus
the square root
of 
b squared
minus 4ac,
and that whole thing
is over 2a.
So now I'm ready 
to plug my values in.
So I get x equals
negative...
b is a negative 1,
so there's my 
negative b,
plus or minus
the square root
of...
b is negative 1,
squared
minus 4
times...
'a' is 2...
minus 4ac and 
c is a negative 1.
And that's all over
2a...
'a' is 2.
So doing the math for this,
I'm going to get x equals
negative negative 1 
is a positive 1,
plus or minus...
negative 1 squared is 1,
minus 4 times 2... 
Negative 4 times 2 is negative 8,
and then negative 8 times 
negative 1
is positive 8,
and that's all going to over 
2 times 2, which is 4.
So,
I can combine 
the 1 and the 8.
I'll get 1
plus or minus the 
square root of 9
over 4,
and the square root 
of 9 is 3.
So I can simplify this 
even more to 1
plus or minus
3
over 4.
Now,
Since I've got a plus or minus, 
let's figure out what the plus
value would be, and what 
the minus value would be.
So I'm 
going to have 
x equals
1
plus 3
over 4
and x equals 
1 minus 3 
over 4.
Well, 1 plus 3 is 4,
so x
equals
4 over 4.
So x equals 1.
Or,
1 minus 3 is negative 2.
So x equals negative 2 over 4, 
and I can reduce that.
That's going to be 
a negative 1/2.
So my solution is going to be 
x equals 1 or
negative
1/2.
Now let me review 
what I did.
I got all of my terms on one side of the
equation. It doesn't matter which side you
put them on.
I
identified by a, b, and c values.
I wrote my
quadratic formula,
and I plugged those a, b, and c values 
into the quadratic formula.
I did the math
and I came up with my answer 
at the bottom of the page here.
Now there's a point 
I want to make.
Let's look at that 
whole equation again.
So, I'm gonna 
do this again,
but
I'm gonna do it 
much simpler.
So I'm going to get 0 equals
2x squared minus x minus 1.
Now, if you're told to use 
the quadratic formula
then do what we just did. 
If you're not,
take a look and see 
if you can solve this.
As it turns out,
I can take this
and break it down
into... 2x squared 
must have been 2x
times x,
and the only way to make a negative 1 
would be a 1 times 1,
and since that was a negative, I need to 
put a negative sign in for one of these
and a positive sign
for the other.
And if I put a 
negative sign here
and a positive sign here,
I'm going to get back
to this original trinomial.
So I've now got it factored.
You can check this by
multiplying it back, 
by FOILing it back to make sure that
it came from 
the original one.
And now I'll just 
solve this.
So I get 2x plus 1
equals 0,
and x minus 1
equals 0.
So I'll subtract 1 
from each side over here,
and I'm going to get 2x
equals
negative 1.
Divide both sides by 2
and I'm going to get x equals
negative 1/2.
For this equation, 
I'll add 1 to both sides.
I'm going to get x equals 1. 
So my solution is going to be x equals
negative 1/2
and 1.
So the point I want 
to make is this...
If you have to use the quadratic formula, 
either because you're told to use it on a test
or because you can't solve an equation
any other way, then use the quadratic formula.
But before you jump into, take a look 
and see what you've got. It might 
be a lot faster and a lot less steps
and a lot
less dangerous, less of the chance of 
making a mistake because there's less 
steps, if you just factor it by 
some other method.
Okay, so that's about it.
get plenty of practice with this. You're going 
to use the quadratic formula quite a bit
in the math you're going to do
in your current course 
and in future courses.
So make sure you 
understand it well.
Take care. I'll see you next time.
