To solve the quadratic equation using square roots, we start with the given equation:
\[ \frac{-9 + (x - 3)^2}{-4} = -4 \]
First, we can multiply both sides of the equation by -4 to eliminate the fraction:
\[ -9 + (x - 3)^2 = 16 \]
Next, we'll move -9 to the other side of the equation:
\[ (x - 3)^2 = 16 + 9 \]
\[ (x - 3)^2 = 25 \]
Now, we take the square root of both sides:
\[ x - 3 = \pm 5 \]
This gives us two equations to solve:
- \(x - 3 = 5\)
- \(x - 3 = -5\)
Solving the first equation:
\[ x = 5 + 3 = 8 \]
Solving the second equation:
\[ x = -5 + 3 = -2 \]
Therefore, the solutions to the equation are:
\[ {8, -2} \]
The correct answer is:
\({8, -2}\)