In this presentation, we will look at an
example of solving an equation using the
quadratic formula.  So our equation we're
interested in solving is X squared plus
13 equal to 6X.  So in order to apply the
quadratic formula, our first step is we
have to set the equation equal to 0. 
So we'll have to subtract the 6X over to
the left side of the equation.  So we
could rewrite the equation as X squared
minus 6X plus 13 equal to 0.  And now I
think it's useful to write down the
quadratic formula.  This is helpful for us. 
So X is equal to - the solutions are given
by: minus b, or the opposite of b, plus or
minus, the square root of b squared minus
4 times a times c, all over 2 times a.  So
this quadratic formula is definitely
worthwhile knowing: the opposite of b,
plus or minus, the square root of b
squared minus 4ac, all over 2a.  So now
what we have to do is decide what the a,
b, and c are in our equation.  So the a is
the coefficient of the X squared term.  So a
would be 1.  The b is the coefficient of
the X term, which would be minus 6; and the c
is the constant term, which would be 13.
 And now that we have identified a, b and
c, we're ready to plug into the formula. 
So X would equal: the opposite of b, which
would be the opposite of negative 6; plus
or minus, the square root b squared would
be minus 6 squared; minus 4ac, 4 times 1
times c, which is 13.  And this is all
divided by 2 times a, which would be 2
times 1.  So now we have to just simplify
our answer.  And so the first part, when we take a [an]
opposite of negative 6, so that would
make it 6;  plus or minus, when we
simplify the square root: minus 6 squared
is 36, minus 4 times 1 times 13 would be 52;
all over 2 times 1, which is 2.  And
simplifying the radical, this is 6
plus or minus, the square root of minus 16, over 2.  And so now at this point, we want to
simplify the radical first, and then
we'll try to simplify the fraction at
the next step.  So simplifying the radical,
so we bring the 6 along, plus or minus
square root of minus 16.  The fact that
it's a negative under the radical tells
us we have to write it with an i, and
the square root of 16 works out to
be 4.  So the square root of minus 16
works out to be four times i or 4i.  So
the i is because we're talking about
the square root of a negative number.  We
have to use the i, and then the square
root of 16 works out to be 4.
And then this is all divided by 2.  And now
that the radical is simplified, now we can
simplify the fraction.   And if we divide
everything by 2, we would end up with
3 plus or minus 2i over 1, which we
can just write as 3 plus or minus 2i .
And so this would be our final solution: 3
plus or minus 2i.  So in this case our
solutions happen to be complex numbers.
