To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can first recognize that the left-hand side can be expressed as a square of a binomial.
The equation can be rewritten as:
\[ x^2 - 16x + 64 = (x - 8)^2 \]
This follows because:
\[ (x - 8)(x - 8) = x^2 - 8x - 8x + 64 = x^2 - 16x + 64 \]
Now, we can set the squared term equal to zero:
\[ (x - 8)^2 = 0 \]
To solve for \( x \), we take the square root of both sides:
\[ x - 8 = 0 \]
Adding 8 to both sides gives:
\[ x = 8 \]
Thus, the solution to the quadratic equation \( x^2 - 16x + 64 = 0 \) is:
\[ \boxed{8} \]
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