To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can first recognize that the left side of the equation can be factored.
The equation can be rewritten as:
\[ (x - 8)^2 = 0 \]
This is because \( (x - 8)(x - 8) = x^2 - 16x + 64 \).
Now, we set the equation equal to zero:
\[ (x - 8)^2 = 0 \]
Taking the square root of both sides gives us:
\[ x - 8 = 0 \]
Solving for \( x \) yields:
\[ x = 8 \]
Thus, the solution to the equation \( x^2 - 16x + 64 = 0 \) is \( x = 8 \).
The response is: x=8