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Solve the equation. Express numbers in exact simplest form. \[ x^{3}-49 x=0 \] The solution set is \( \{\square\} \).

Ask by May Daniels. in the United States
Mar 09,2025

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The solutions are \( x = -7 \), \( x = 0 \), and \( x = 7 \).

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To solve the equation \( x^3 - 49x = 0 \), we can factor out an \( x \): \[ x(x^2 - 49) = 0 \] This gives us two factors to set to zero: 1. \( x = 0 \) 2. \( x^2 - 49 = 0 \) For the second factor, we can solve for \( x \): \[ x^2 = 49 \quad \Rightarrow \quad x = \pm 7 \] Thus, the complete solution set is: \[ \{ -7, 0, 7 \} \]

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