To solve the equation \(25x^2 - 196 = 0\) using the difference of squares pattern, we can first rewrite the equation in a factored form. Notice that this equation can be expressed as a difference of squares:
\[ 25x^2 - 196 = (5x)^2 - (14)^2 \]
According to the difference of squares formula, \(a^2 - b^2 = (a - b)(a + b)\), we can factor the equation as follows:
\[ (5x - 14)(5x + 14) = 0 \]
Setting each factor to zero gives us the possible solutions:
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\(5x - 14 = 0\)
- \(5x = 14\)
- \(x = \frac{14}{5}\)
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\(5x + 14 = 0\)
- \(5x = -14\)
- \(x = -\frac{14}{5}\)
Thus, the correct solutions are:
\[ x = \frac{14}{5} \quad \text{and} \quad x = -\frac{14}{5} \]
Among the choices provided, the closest match would be:
- \(x = - \frac{14}{5}, x = \frac{14}{5}\)
Therefore, the correct response is:
x = -\( \frac{14}{5} \), x = \( \frac{14}{5} \).
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