To solve the equation \( 64x^2 + 9 = 13 \) by factoring using the difference of squares pattern, we first move all terms to one side of the equation:
\[ 64x^2 + 9 - 13 = 0 \]
This simplifies to:
\[ 64x^2 - 4 = 0 \]
Next, we notice that \( 64x^2 - 4 \) is a difference of squares, which can be factored as follows:
\[ (8x - 2)(8x + 2) = 0 \]
Setting each factor equal to zero gives us:
- \( 8x - 2 = 0 \)
- \( 8x + 2 = 0 \)
Solving the first equation:
\[ 8x = 2 \implies x = \frac{2}{8} = \frac{1}{4} \]
Solving the second equation:
\[ 8x = -2 \implies x = \frac{-2}{8} = -\frac{1}{4} \]
Hence, the solutions are:
\[ x = \frac{1}{4}, \quad x = -\frac{1}{4} \]
Among the provided responses, the one that correctly indicates the solutions is:
x = -Start Fraction 1 over 4 End Fraction, x = Start Fraction 1 over 4 End Fraction.