To solve the equation \( 49x^2 - 225 = 0 \) by factoring using the difference of squares pattern, we can rewrite it as follows:
- Recognize that \( 49x^2 - 225 \) is a difference of squares since \( 49x^2 = (7x)^2 \) and \( 225 = 15^2 \).
- Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we can factor the expression:
\[ 49x^2 - 225 = (7x - 15)(7x + 15) = 0 \]
- Now, set each factor to zero and solve for \( x \):
\[ 7x - 15 = 0 \quad \Rightarrow \quad 7x = 15 \quad \Rightarrow \quad x = \frac{15}{7} \]
\[ 7x + 15 = 0 \quad \Rightarrow \quad 7x = -15 \quad \Rightarrow \quad x = -\frac{15}{7} \]
Thus, the solutions are:
\[ x = \frac{15}{7} \quad \text{and} \quad x = -\frac{15}{7} \]
Given the options, the correct response is:
x equals negative Start Fraction 15 over 7 End Fraction, x equals Start Fraction 15 over 7 End Fraction.
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