To solve the equation \(-x^4 - 2 = -10\), we first isolate the term involving \(x\).
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Add 2 to both sides of the equation: \[ -x^4 - 2 + 2 = -10 + 2 \] Simplifying this gives: \[ -x^4 = -8 \]
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Multiply both sides by -1 to eliminate the negative sign: \[ x^4 = 8 \]
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Now take the fourth root of both sides: \[ x = \pm \sqrt[4]{8} \] This can be simplified: \[ \sqrt[4]{8} = \sqrt[4]{2^3} = 2^{3/4} = 2^{0.75} = \sqrt{2^3} = \sqrt{(2^2)(2)} = 2\sqrt{2} \] Thus, \(x = \pm 2\sqrt{2}\).
Since none of the provided options match \(2\sqrt{2}\) (approximately \(2.83\)) or its negative, please check the answers provided. But you can confirm that the correct answer should be written as \(x = \pm 2\sqrt{2}\) or in decimal form it is approximately \(x \approx 2.83\) or \(x \approx -2.83\).
None of the options \(32\), \(-2\), \(3\), or \(48\) are accurate for this equation.