Today we'll be solving the equation
x squared plus eight
x plus 25 equals zero.
Now, to solve for x in this equation,
we'll have to use the quadratic formula.
Here it is, up in the right.
So let's plug in our values.
We get x equals negative eight
plus or minus the square root
of eight squared minus four times 25
times one divided by two times one.
This gives us negative eight
plus or minus the square root
of 64 minus 100,
all divided by two.
Now, 64 minus 100 is negative 36.
This gives us the square root
of a negative number in our
answer, which we can't do,
so there are actually no solutions.
But we can include the complex numbers
if we break up our square
root as the square root of 36
times the square root of negative one.
The square root of 36 is six,
and the square root of negative one is i.
So replacing the square
root of negative 36
with six i gives us negative eight
plus or minus six i divided by two.
These can be broken up
into their own fractions
of negative eight over two
plus or minus six i over two.
This gives us x equals negative
four plus or minus three i.
So these are the complex
solutions to our equation.
