To solve the equation \((x + 4)^2 = -11\) using the square root property, we start by isolating the square on one side, which it already is in this case.
According to the square root property, if \(a^2 = b\), then \(a = \sqrt{b}\) or \(a = -\sqrt{b}\).
However, in this case, we have \(b = -11\), which is negative. Taking the square root of a negative number indicates that the solutions will be complex numbers.
We will take the square root of both sides:
\[ x + 4 = \pm \sqrt{-11} \]
The square root of \(-11\) can be expressed as:
\[ \sqrt{-11} = i\sqrt{11} \]
So we rewrite the equation:
\[ x + 4 = \pm i\sqrt{11} \]
Now, we will isolate \(x\):
\[ x = -4 \pm i\sqrt{11} \]
The solutions to the equation are:
\[ x = -4 + i\sqrt{11} \quad \text{and} \quad x = -4 - i\sqrt{11} \]
Thus, the final solutions are:
\[ x = -4 + i\sqrt{11} \quad \text{and} \quad x = -4 - i\sqrt{11} \]