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Question Grant was asked to solve 49x2−225=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point) Responses x=−715 , x=715 x is equal to negative 7 over 15, x is equal to 7 over 15 - no response given x=−157 x is equal to negative 15 sevenths - incorrect x=22549 , x=−22549 x is equal to 225 over 49, x is equal to negative 225 over 49 - no response given x=−157 , x=157

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To solve the equation \(49x^2 - 225 = 0\) using the difference of squares, we can follow these steps:

  1. Recognize the difference of squares: The expression \(49x^2 - 225\) can be factored as \((7x)^2 - 15^2\). This fits the difference of squares pattern \(a^2 - b^2 = (a - b)(a + b)\), where \(a = 7x\) and \(b = 15\).

  2. Factor the equation: \[ 49x^2 - 225 = (7x - 15)(7x + 15) = 0 \]

  3. Set each factor equal to zero: \[ 7x - 15 = 0 \quad \text{or} \quad 7x + 15 = 0 \]

  4. Solve each equation:

    • For \(7x - 15 = 0\): \[ 7x = 15 \quad \Rightarrow \quad x = \frac{15}{7} \]
    • For \(7x + 15 = 0\): \[ 7x = -15 \quad \Rightarrow \quad x = -\frac{15}{7} \]

  5. Final answers: The solutions for the equation \(49x^2 - 225 = 0\) are: \[ x = \frac{15}{7} \quad \text{and} \quad x = -\frac{15}{7} \]

From the responses you provided, the correct answers corresponding to our solutions are:

  • \(x = \frac{15}{7} \)
  • \(x = -\frac{15}{7} \)

So the correct response should identify those solutions (though it seems they were not explicitly given among the options).