Today we'll be solving for x
in the equation x squared
plus 18 equals six x.
Our first step is to move
everything to be on the same side,
so we'll move that six x.
That gives us x squared minus
six x plus 18 equals zero.
Now that it's set equal
to zero, we can solve.
This can't be factored,
so we'll have to use
the quadratic equation.
And plugging in our values,
we get x equals positive six
plus or minus the square
root of negative six squared
minus four times 18 times one,
all divided by two times one.
Working this out, this
gives us x equals six
plus or minus the square
root of 36 minus 72,
all divided by two.
36 minus 72 is negative 36,
and we can't take the square
root of a negative number.
So this equation has no real solutions,
but we can find the complex solutions
by breaking up the square
root of negative 36
into the square root of 36
times the square root of negative one.
This gives us six times i.
And plugging that back into our equation,
we get x equals six
plus or minus six i divided by two.
Breaking these up into separate fractions,
we get x equals six over two
plus or minus six i over two.
And simplifying this gives
us our complex solutions
three plus or minus three i.
