To solve the equation \(36x^2 - 64 = 0\) using the difference of squares pattern, let's first rewrite the equation in a recognizable form.
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Notice that the expression \(36x^2 - 64\) can be factored as a difference of squares: \[ 36x^2 - 64 = (6x)^2 - (8)^2 \]
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We can then apply the difference of squares formula, which is \(a^2 - b^2 = (a - b)(a + b)\), where \(a = 6x\) and \(b = 8\): \[ (6x - 8)(6x + 8) = 0 \]
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This gives us two equations to solve: \[ 6x - 8 = 0 \quad \text{and} \quad 6x + 8 = 0 \]
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Solving the first equation: \[ 6x - 8 = 0 \implies 6x = 8 \implies x = \frac{8}{6} = \frac{4}{3} \]
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Solving the second equation: \[ 6x + 8 = 0 \implies 6x = -8 \implies x = \frac{-8}{6} = -\frac{4}{3} \]
Thus, the solutions to the equation \(36x^2 - 64 = 0\) are: \[ x = \frac{4}{3} \quad \text{and} \quad x = -\frac{4}{3} \]
So the correct response is: x equals \(\frac{4}{3}\) and x equals negative \(\frac{4}{3}\).