Today we'll be solving
for x in the equation
x squared minus four
x plus 29 equals zero.
Since this quadratic cannot be factored,
we're going to have to
use the quadratic formula.
So plugging in our values here,
we get X equals positive
four plus or minus
the square root of negative four squared
minus four times 29 times one,
all divided by two times one.
Now working this out
under the square root,
we get x equals four plus or
minus the square root of 16
minus 116, all divided by two.
Now 16 minus 116 gives us negative 100.
We can't take the square
root of a negative,
so this equation has no real solutions.
But we can find the complex solutions
by breaking up the square
root of negative 100,
into the square root of 100
times the square root of negative one.
This gives us 10 times i,
and plugging this back into our solution,
we get x equals four plus
or minus 10i over two.
Breaking them up into separate fractions,
we get x equals four over two
plus or minus 10i over two.
We can simplify this to give us
x equals two plus or minus five i.
So these are complex solutions.
