To solve the equation \(25x^2 - 196 = 0\) using the difference of squares pattern, we can rewrite it as:
\[ 25x^2 - 196 = (5x)^2 - (14)^2 = 0 \]
Now we can apply the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\):
\[ (5x - 14)(5x + 14) = 0 \]
Setting each factor equal to zero gives us the solutions:
-
\(5x - 14 = 0\) \[ 5x = 14 \implies x = \frac{14}{5} \]
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\(5x + 14 = 0\) \[ 5x = -14 \implies x = -\frac{14}{5} \]
Thus, the solutions are:
\[ x = \frac{14}{5} \quad \text{and} \quad x = -\frac{14}{5} \]
In summary, the correct responses are:
- \(x = -\frac{14}{5}, x = \frac{14}{5}\)