>> All right, the
almighty quadratic formula,
so famous it has songs
written about them.
If you go on YouTube you'll
actually see some of them.
There are also phrases,
and my favorite phrase is the
negative boy couldn't decide
whether to go to
the radical party
where the square bouncer
removed four alcoholic cans
and it was all over around
two a.m. But no matter what,
any way you want to use to
memorize this, you still need
to memorize it, it's
used very often.
All right, and where it comes
from is our basic quadratic has
to be equal to zero, and
the first coefficient is a,
the second is b, and
always include the sign,
and the third is c. Okay,
so now all you have
to do is plug it in.
So it's negative and then
the b here is negative 3,
plus or minus square
root, same thing,
make sure you put everything in
parentheses as you write them.
So our a is 2, our c is negative
4, and then it's all over,
very important, all over
2 over 2, 2 times 2.
All right, so the
main complicated thing
on these problems is always
the radical, and so that's
where you want to start.
You want to take the radical
and write it off to the side,
and you can simplify
it before you write it.
So negative 3 squared is 9,
minus 4 times 2,
times negative 4.
And this second part here,
you want to multiply
it all together.
So I always go backwards,
that's negative 8,
negative 8 times 4
would be negative 32,
and then change the sign.
So if you see that they have
the same number of signs,
an even number of signs,
it's going to be plus 32.
And then we add those
together, and there we go.
It's better because, see,
there's multiple steps,
and if you were to
keep writing you have
to keep writing everything,
but this way you just
simplify the radical
and you can go on
to the next part.
So opposite of a
negative is positive,
and that's it, and
now it's done.
So it's nice and
clean and simple
if you simplify the
radical first.
All right, let's
try another one.
So the first step on
this is to make it look
like our nice quadratic,
which means we have
to set it equal to zero.
So it's k squared, minus
6k, minus 3, equals zero.
You have to subtract
the 3 to the other side.
And then we write our
formula, and it's good
to just keep writing it, that's
the best way to memorize this.
All right, now we plug it in.
So we're going to plug in a b,
another b squared,
a, c all over 2a.
All right, so we need to write
our a x squared minus bx,
plus c, there you go,
plus, everything is plus.
So our a goes here and that's 1.
That's our b, and
that's our c, okay?
So the b is minus 6, the a is 1,
and the b is minus 3, or the c,
sorry, the c is minus 3.
We'll circle that, there we go.
so one more time, b, b, a,
c and a. Okay, we're good.
So like I said before start
with the radical, so that's 36.
This one will always
become positive
because we're squaring it, minus
4 times 1 times negative 3.
And again negative
negative will be plus,
and that's 12, so that's 48.
And there's our radical
that we need to simplify.
So 48 is made up of 4 and
12 or we can do 6 and 8,
which is probably cleaner,
2 and 3, 2 and 4, 2 and 2.
All right, so we have square
root of four 2's and a 3,
so that's 2 and 2,
that's 4 rad 3.
Okay, so let's put it all
back together, that's 6 plus
or minus 4 radical
3, all over 2.
Now you would think it's
done, just like before,
but they all contain a number
that's in common, which is 2,
which means we have
to keep going.
We need to factor out that
number on top, double-check it,
that's 6, that's 4, and
reduce, and there you go.
Now the reason we have
to reduce it is it's just
like any other fraction,
we want the simplest form.
And so if they all contain
a common factor we need
to factor it out and cancel.
All right, here's the last
one to try, give it a shot.
Hit pause, by the way.
All right, so you should
have gotten this far.
So if you plug everything
in we get this.
If you notice there's
no radicals left,
which means we're going to get
nice real rational numbers.
So we have to separate
it and simplify.
So that would give us x
equals, that's 16 over 40,
and then they have a 4 in
common, next we have an 8,
so that would be 2 over 5,
and then x equals negative 10
over 40, which is
negative one-fourth.
So we get x equals
negative one-fourth
or x equals two-fifths.
And those are your answers,
so if you can simplify
it you should.
What this means is that
this is actually factorable,
and there is the
factored form of it.
So you could also have
factored this instead,
and this just reminded me of one
thing, we're solving for y here,
we can't use x, we've got to use
y equals, y equals, y equals y,
y, and so on because we're
solving for y, not x. Same thing
up here, this is not
an x, this is a k,
and there we go, much better.
All right, so again if you
have a radical and it's done,
you don't have to simplify
it, you're finished.
If you have a common factor
make sure you factor out
and reduce it, and if
there are no radicals,
that it's a nice rational
number then you must simplify it
and find those rational
numbers, and that's everything.
That's everything
for quadratics.
Thanks.
