To solve the equation \( x^2 - 6x + 25 = 0 \), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1 \), \( b = -6 \), and \( c = 25 \).
First, let's calculate the discriminant:
\[ b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 25 = 36 - 100 = -64 \]
Since the discriminant is negative, this means the solutions will be complex numbers.
Now we can substitute the values into the quadratic formula:
\[ x = \frac{6 \pm \sqrt{-64}}{2 \cdot 1} \]
This simplifies to:
\[ x = \frac{6 \pm 8i}{2} \]
Now simplifying further:
\[ x = 3 \pm 4i \]
So the solutions are:
\[ x = 3 + 4i \quad \text{and} \quad x = 3 - 4i \]
The answer matches with option A: \( 3 \pm 4i \).
So the final answer is:
A. \( 3 \pm 4i \)