- [Phillip Clark] In this
video, we're gonna look at
solving a quadratic equation
using the quadratic formula.
So this is a basic example,
but it applies to much
more difficult examples
with much larger coefficients.
As a reminder, quadratic
formula solves for x
that makes the quadratic zero.
It is minus b,
plus or minus the square root
of b squared minus 4ac...
All over 2a.
So all we have to do is
identify the a, b, and c in this problem,
and we'll be finished.
So a is the coefficient of
x squared, so a equals one.
B is the coefficient of
x, so b equals eight.
And C is whatever our
constant coefficient is,
in this case it's two.
And there's our a, b, and c.
So, now x equals negative eight, for b,
plus or minus the square root
of negative eight squared
minus four times a, which was
one, times c, which was two.
All over two times one.
Now it it important to do all over that.
This whole piece up here
is the whole numerator.
Equals negative eight plus
or minus the square root
negative eight squared is a positive 56,
minus four times two is minus eight.
Sorry, negative eight squared is 64.
A step ahead.
All over two times one, which is two.
Negative eight plus or minus
the square root of 56 all over two.
Now we're gonna simplify completely,
so what we're gonna do in
that piece under the radical
since it's not a perfect square itself,
we look to see if it has any factors
that are perfect squares.
So for instance, I can
pull a four out of here.
And rewrite this as four times 14.
Now, 14 could be factored further,
but it has no perfect squares as factors.
So that's as far as we need to go.
Now the property of
exponents we'll be using here
is we can split up a
radical over multiplication.
So I can rewrite this as
the square root of four
times the square root of 14, all over two.
Square root of four,
we know, it's just two.
So we can rewrite this as negative eight
plus or minus two, times the
square root of 14 all over two.
Now, it's very tempting to just
cancel this two and this two.
We can't do that.
But, there's a factor of two
in both terms on top, so that's good.
Basically what we're gonna do,
is we're gonna factor a two out of the top
and rewrite it as minus
four plus or minus rad 14
all over two, and now we can cancel
because now we have a product.
So our simplified answer is minus four
plus or minus rad 14.
Okay, and that's nice and simplified
and that's as far as we can go.
So those are the two zeroes,
one for plus one for
minus of our quadratic.
