To solve the equation \( x^3 - 9 = 6 \), we can start by isolating the \( x^3 \) term.
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Add 9 to both sides of the equation: \[ x^3 - 9 + 9 = 6 + 9 \] This simplifies to: \[ x^3 = 15 \]
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Now, take the cube root of both sides to solve for \( x \): \[ x = \sqrt[3]{15} \]
So, the solution is: \[ x = \sqrt[3]{15} \]