To solve the equation \( 25x^2 - 196 = 0 \) by factoring using the difference of squares pattern, we can recognize that the equation can be rewritten in the form \( a^2 - b^2 = 0 \).
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Identify \( a \) and \( b \):
- Here, \( a^2 = 25x^2 \) implies \( a = 5x \)
- And \( b^2 = 196 \) implies \( b = 14 \)
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The equation can then be factored as follows: \[ (5x - 14)(5x + 14) = 0 \]
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Now, set each factor equal to zero: \[ 5x - 14 = 0 \quad \text{or} \quad 5x + 14 = 0 \]
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Solving these equations:
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From \( 5x - 14 = 0 \): \[ 5x = 14 \implies x = \frac{14}{5} \]
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From \( 5x + 14 = 0 \): \[ 5x = -14 \implies x = -\frac{14}{5} \]
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Therefore, the solutions are \( x = \frac{14}{5} \) and \( x = -\frac{14}{5} \).
The correct response is:
x = -14/5, x = 14/5