To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we first identify if the equation can be expressed as a perfect square.
The general form of a perfect square trinomial is:
\[ (a - b)^2 = a^2 - 2ab + b^2 \]
In our equation:
- The first term, \( x^2 \), corresponds to \( a^2 \) where \( a = x \).
- The constant term \( 64 \) corresponds to \( b^2 \), hence \( b = 8 \) since \( 8^2 = 64 \).
- The middle term \( -16x \) corresponds to \( -2ab \), so we can verify this:
\[ -2ab = -2(x)(8) = -16x \]
This confirms the equation can be expressed as a perfect square. Therefore, we rewrite the equation:
\[ (x - 8)^2 = 0 \]
Next, we solve for \( x \) by taking the square root of both sides:
\[ x - 8 = 0 \]
Thus,
\[ x = 8 \]
Finally, we conclude that the solution to the quadratic equation \( x^2 - 16x + 64 = 0 \) is:
\[ \boxed{8} \]