To solve the quadratic equation \(x^2 - 16x + 64 = 0\) using the perfect square trinomial pattern, we first recognize that the given equation can be rewritten as a perfect square.
Recall that a perfect square trinomial is of the form \((a - b)^2 = a^2 - 2ab + b^2\).
In your equation \(x^2 - 16x + 64\):
- Identify \(a\): The coefficient of \(x\) is \(-16\), so half of that is \(-8\).
- Identify \(b^2\): The last term is \(64\), which is \(8^2\).
This means that the equation can be rewritten as:
\[ (x - 8)^2 = 0 \]
Now, we can take the square root of both sides:
\[ x - 8 = 0 \]
Solving for \(x\), we get:
\[ x = 8 \]
Thus, the solution to the quadratic equation \(x^2 - 16x + 64 = 0\) is
\[ \boxed{8} \]