To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can start by rewriting the quadratic in the form of a perfect square.
Notice that: \[ x^2 - 16x + 64 = (x - 8)^2 \] This is because \( (x - 8)(x - 8) = x^2 - 16x + 64 \).
Now, we can set the equation equal to zero: \[ (x - 8)^2 = 0 \]
Taking the square root of both sides, we get: \[ x - 8 = 0 \]
Solving for \( x \), we find: \[ x = 8 \]
Thus, the solution to the quadratic equation \( x^2 - 16x + 64 = 0 \) is \[ \boxed{8} \]
Among the options provided: a) \( x = 8 \) is the correct answer.