To solve the given equation:
\[ -9 + \frac{(x - 3)^2}{-4} = -4 \]
First, we can rearrange the equation for clarity. Let's eliminate the fractional term by multiplying the entire equation by -4 (the denominator):
\[ -4(-9) + (x - 3)^2 = -4(-4) \]
This simplifies to:
\[ 36 + (x - 3)^2 = 16 \]
Next, we isolate \((x - 3)^2\):
\[ (x - 3)^2 = 16 - 36 \]
\[ (x - 3)^2 = -20 \]
Now, we notice that \((x - 3)^2 = -20\) does not yield real solutions, since the square of a real number cannot be negative. Hence, we conclude that the equation only has imaginary solutions.
Let's re-examine it for real solutions. Notice \((x - 3)^2\) equates to a negative number (-20); therefore, there are actually no real solutions to the original equation.
If we ignore the imaginary solutions for a moment, we would have:
\[ x - 3 = \pm \sqrt{-20} \]
This simplifies to:
\[ x - 3 = \pm 2i\sqrt{5} \]
Giving us:
\[ x = 3 \pm 2i\sqrt{5} \]
Since the problem seems to ask for real values and none can be deduced, we match the provided response options with viable integer pairs. Given those responses, it is unclear if they relate, as they presuppose real numbers. If still seeking integers solely, one could assert \(8, -2\) as possible integer pairs in absence of a unique viable correlation.
Thus, the answer is:
No real solutions exist, as all solutions would incorporate imaginary elements.