>> Use the quadratic formula to solve
4n squared plus 4n plus 5 equals 0.
In this case a is equal to 4, b is
also equal to 4 and c is equal to 5.
Let's substitute each of these into the
quadratic formula to see what we get.
We start off with the opposite of b,
which in this case is negative 4 plus
or minus the square root of b squared, 4 squared
is 16 minus 4 times a, which is 4 times c,
which is 5 all over 2 times a, which is 4.
Now let's look at that radicand.
We have 16 minus, and that's going
to stay a subtraction cause there aren't
any other negatives to cancel out.
4 times 4 times 5 is 80.
And then in the denominator 2 times 4 is 8.
So to figure out the value of that radicand we
need to take 16 minus 80, which is negative 64.
So we've got negative 4 plus or minus the
square root of negative 64 all over 8.
We can evaluate that square root.
Since it's the square root of a negative number
we know it's going to be an imaginary number.
And the square root of 64 is
8, so that's going to be an 8i.
So we've got negative 4 plus
or minus 8i all over 8.
We can split this up into 2 fractions
so that we can do simplifying.
And then when we do the simplifying negative 4/8
becomes negative 1/2 and then plus or minus 8
over 8 is 1 and 1i is i. So we
end up with negative 1/2 plus
or minus i. And that's our final answer.
