 
Hello.
Professor Poyser here and I
want to work out a quick
problem for solving a quadratic
equation and using
the quadratic formula.
I'll show you how this works.
First of all, I hope you
realize that this is an
equation because of
the equal sign.
And it's not just an equation,
but a quadratic equation
because the largest
exponent is a 2.
So to use this quadratic
formula, I should probably
write that down for you.
And it's a good thing
for you to memorize.
The formula is x is equal to
negative b, or sometimes
that's read as the opposite of
b, plus or minus the square
root of b squared minus
4ac all over 2a.
So this formula here, the
quadratic formula,
uses a b and c.
So back to our quadratic
equation.
We need to know what
a, b, and c are.
Well to do that, this equation
should really be
set equal to 0.
So I tell you what.
Let's bring that 7 over to the
other side, first which then
makes the equation 2y squared
minus 3y minus 7 equals 0.
So now that we have in that form
there, we can easily see
that a is 2, b is negative
3, and c is negative 7.
All I'm doing here is I'm just
picking off the coefficients
for each of these terms there.
The a is the coefficient
of the squared term.
The b is the coefficient of the
variable of just y or x,
that's all by itself.
And the c is the
constant term.
That's on the same side.
So now I have my players a, b,
and c, it's just a matter of
just plugging them into
our quadratic formula.
Here it goes.
So I have x is equal to, and the
way I read this is, give
me the opposite of b.
So since our b is negative 3,
the opposite would be a
positive 3.
or minus b squared.
All right, b squared that's just
negative 3 times itself
which is 9, minus 4 times
a couple of numbers.
What are those numbers?
Those numbers are a and c.
So it's 2 and negative 7.
And I'm going to draw a big old
fraction bar there, and on
the bottom is 2 times a.
And again our a is 2, so
our denominator is
just simply a 4.
Hope you see that.
Well, what I would work
out first, in
this formula, is this.
Let's start inside of
that radical sign.
Let's start inside that big old
square root because if all
of this stuff turns into a
negative number, we can
automatically stop because a
negative number inside of a
square root is not real.
That kicks into the imaginary
which we're not
doing in MAT 099.
So let's see, I guess I would
do the multiplication first.
Right?
Please Excuse My Dear Aunt Sally
means to multiply this 4
times 2, which is 8.
And 8 times that negative
7 is a negative 56.
Write that down right there.
And don't forget my denominator
is 2 times 2,
which is 4.
OK well this is 9 minus a
negative 56, which is really
the same thing as saying
9 plus 56 and 9
plus is 56 is a 65.
So we're almost done.
What I have then is 3
plus or minus square
root of 65 over 4.
Now I know that I cannot
simplify 65 anymore because if
I try to break it down, if I try
to factor it, you'll see
that it's just 5 times 13.
No identical pairs there that
I could pull out of that
square root.
So I know that radical 65 or
square root 65 is as simple as
I can get it.
Now on MyMathLab, if you're
doing this homework assignment
on MyMathLab, let me just scoot
this down so you can see
a little better, there is
no plus or minus button.
So we have to enter in this
answer on MyMathLab inside the
box that they give
us in two ways.
So the first way is going to be,
3 plus the square root of
65 all over 4 comma.
And then 3 minus the square
root of 65 all over 4.
That's what you're going to
enter in on MyMathLab as your
2 answers because there's
no plus or minus button.
We have to write it twice,
separated by a comma.
So on MyMathLab, I would start
with the fraction button
first, enter this in
the numerator.
Put the 4 in the bottom.
Get out of that fraction.
Put the comma.
And then continue there.
Put another fraction, 3 minus
square root of 65 all over 4.
Answer to that problem.
 
