To solve the quadratic equation \(64x^2 - 80x + 25 = 0\) using the perfect square trinomial pattern, we first observe that the equation might be factored as a perfect square.
The general form of a perfect square trinomial is:
\[ (a - b)^2 = a^2 - 2ab + b^2 \]
In this case, let's rewrite the given equation:
\[ 64x^2 - 80x + 25 \]
This can be rearranged as:
\[ (8x)^2 - 2(8x)(5) + (5)^2 \]
This indicates it can be factored as:
\[ (8x - 5)^2 \]
Now, we rewrite the initial equation:
\[ (8x - 5)^2 = 0 \]
Next, we take the square root of both sides:
\[ 8x - 5 = 0 \]
Now we can solve for \(x\):
\[ 8x = 5 \ x = \frac{5}{8} \ x = 0.625 \]
Thus, the solution to the quadratic equation \(64x^2 - 80x + 25 = 0\) is:
x equals 0.625.