To solve the equation $x^2 + 100 = 0$ using the square root property, we first isolate the $x^2$ term:

$x^2 = -100$

Next, we apply the square root property, which states that if $x^2 = a$, then $x = \pm \sqrt{a}$. Applying this to our equation:

$x = \pm \sqrt{-100}$

Since we are dealing with the square root of a negative number, the solutions will be complex. We know that $\sqrt{-1} = i$, where $i$ is the imaginary unit. Therefore:

$\sqrt{-100} = \sqrt{100} \cdot \sqrt{-1} = 10i$

Thus, the solutions to the equation are:

$x = \pm 10i$

So, the simplified complex solutions are $x = 10i$ and $x = -10i$.