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Simplifying (3x + -8)(3x + -8)(3x + -8)(3x + -8)(3x + -8)(3x + -8) = 4096 Reorder the terms: (-8 + 3x)(3x + -8)(3x + -8)(3x + -8)(3x + -8)(3x + -8) = 4096 Reorder the terms: (-8 + 3x)(-8 + 3x)(3x + -8)(3x + -8)(3x + -8)(3x + -8) = 4096 Reorder the terms: (-8 + 3x)(-8 + 3x)(-8 + 3x)(3x + -8)(3x + -8)(3x + -8) = 4096 Reorder the terms: (-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x)(3x + -8)(3x + -8) = 4096 Reorder the terms: (-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x)(3x + -8) = 4096 Reorder the terms: (-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 Multiply (-8 + 3x) * (-8 + 3x) (-8(-8 + 3x) + 3x * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 ((-8 * -8 + 3x * -8) + 3x * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 ((64 + -24x) + 3x * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 (64 + -24x + (-8 * 3x + 3x * 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 (64 + -24x + (-24x + 9x2))(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 Combine like terms: -24x + -24x = -48x (64 + -48x + 9x2)(-8 + 3x)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 Multiply (64 + -48x + 9x2) * (-8 + 3x) (64(-8 + 3x) + -48x * (-8 + 3x) + 9x2 * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 ((-8 * 64 + 3x * 64) + -48x * (-8 + 3x) + 9x2 * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 ((-512 + 192x) + -48x * (-8 + 3x) + 9x2 * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 (-512 + 192x + (-8 * -48x + 3x * -48x) + 9x2 * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 (-512 + 192x + (384x + -144x2) + 9x2 * (-8 + 3x))(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 (-512 + 192x + 384x + -144x2 + (-8 * 9x2 + 3x * 9x2))(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 (-512 + 192x + 384x + -144x2 + (-72x2 + 27x3))(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 Combine like terms: 192x + 384x = 576x (-512 + 576x + -144x2 + -72x2 + 27x3)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 Combine like terms: -144x2 + -72x2 = -216x2 (-512 + 576x + -216x2 + 27x3)(-8 + 3x)(-8 + 3x)(-8 + 3x) = 4096 Multiply (-512 + 576x + -216x2 + 27x3) * (-8 + 3x) (-512(-8 + 3x) + 576x * (-8 + 3x) + -216x2 * (-8 + 3x) + 27x3 * (-8 + 3x))(-8 + 3x)(-8 + 3x) = 4096 ((-8 * -512 + 3x * -512) + 576x * (-8 + 3x) + -216x2 * (-8 + 3x) + 27x3 * (-8 + 3x))(-8 + 3x)(-8 + 3x) = 4096 ((4096 + -1536x) + 576x * (-8 + 3x) + -216x2 * (-8 + 3x) + 27x3 * (-8 + 3x))(-8 + 3x)(-8 + 3x) = 4096 (4096 + -1536x + (-8 * 576x + 3x * 576x) + -216x2 * (-8 + 3x) + 27x3 * (-8 + 3x))(-8 + 3x)(-8 + 3x) = 4096 (4096 + -1536x + (-4608x + 1728x2) + -216x2 * (-8 + 3x) + 27x3 * (-8 + 3x))(-8 + 3x)(-8 + 3x) = 4096 (4096 + -1536x + -4608x + 1728x2 + (-8 * -216x2 + 3x * -216x2) + 27x3 * (-8 + 3x))(-8 + 3x)(-8 + 3x) = 4096 (4096 + -1536x + -4608x + 1728x2 + (1728x2 + -648x3) + 27x3 * (-8 + 3x))(-8 + 3x)(-8 + 3x) = 4096 (4096 + -1536x + -4608x + 1728x2 + 1728x2 + -648x3 + (-8 * 27x3 + 3x * 27x3))(-8 + 3x)(-8 + 3x) = 4096 (4096 + -1536x + -4608x + 1728x2 + 1728x2 + -648x3 + (-216x3 + 81x4))(-8 + 3x)(-8 + 3x) = 4096 Combine like terms: -1536x + -4608x = -6144x (4096 + -6144x + 1728x2 + 1728x2 + -648x3 + -216x3 + 81x4)(-8 + 3x)(-8 + 3x) = 4096 Combine like terms: 1728x2 + 1728x2 = 3456x2 (4096 + -6144x + 3456x2 + -648x3 + -216x3 + 81x4)(-8 + 3x)(-8 + 3x) = 4096 Combine like terms: -648x3 + -216x3 = -864x3 (4096 + -6144x + 3456x2 + -864x3 + 81x4)(-8 + 3x)(-8 + 3x) = 4096 Multiply (4096 + -6144x + 3456x2 + -864x3 + 81x4) * (-8 + 3x) (4096(-8 + 3x) + -6144x * (-8 + 3x) + 3456x2 * (-8 + 3x) + -864x3 * (-8 + 3x) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 ((-8 * 4096 + 3x * 4096) + -6144x * (-8 + 3x) + 3456x2 * (-8 + 3x) + -864x3 * (-8 + 3x) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 ((-32768 + 12288x) + -6144x * (-8 + 3x) + 3456x2 * (-8 + 3x) + -864x3 * (-8 + 3x) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 (-32768 + 12288x + (-8 * -6144x + 3x * -6144x) + 3456x2 * (-8 + 3x) + -864x3 * (-8 + 3x) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 (-32768 + 12288x + (49152x + -18432x2) + 3456x2 * (-8 + 3x) + -864x3 * (-8 + 3x) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 (-32768 + 12288x + 49152x + -18432x2 + (-8 * 3456x2 + 3x * 3456x2) + -864x3 * (-8 + 3x) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 (-32768 + 12288x + 49152x + -18432x2 + (-27648x2 + 10368x3) + -864x3 * (-8 + 3x) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 (-32768 + 12288x + 49152x + -18432x2 + -27648x2 + 10368x3 + (-8 * -864x3 + 3x * -864x3) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 (-32768 + 12288x + 49152x + -18432x2 + -27648x2 + 10368x3 + (6912x3 + -2592x4) + 81x4 * (-8 + 3x))(-8 + 3x) = 4096 (-32768 + 12288x + 49152x + -18432x2 + -27648x2 + 10368x3 + 6912x3 + -2592x4 + (-8 * 81x4 + 3x * 81x4))(-8 + 3x) = 4096 (-32768 + 12288x + 49152x + -18432x2 + -27648x2 + 10368x3 + 6912x3 + -2592x4 + (-648x4 + 243x5))(-8 + 3x) = 4096 Combine like terms: 12288x + 49152x = 61440x (-32768 + 61440x + -18432x2 + -27648x2 + 10368x3 + 6912x3 + -2592x4 + -648x4 + 243x5)(-8 + 3x) = 4096 Combine like terms: -18432x2 + -27648x2 = -46080x2 (-32768 + 61440x + -46080x2 + 10368x3 + 6912x3 + -2592x4 + -648x4 + 243x5)(-8 + 3x) = 4096 Combine like terms: 10368x3 + 6912x3 = 17280x3 (-32768 + 61440x + -46080x2 + 17280x3 + -2592x4 + -648x4 + 243x5)(-8 + 3x) = 4096 Combine like terms: -2592x4 + -648x4 = -3240x4 (-32768 + 61440x + -46080x2 + 17280x3 + -3240x4 + 243x5)(-8 + 3x) = 4096 Multiply (-32768 + 61440x + -46080x2 + 17280x3 + -3240x4 + 243x5) * (-8 + 3x) (-32768(-8 + 3x) + 61440x * (-8 + 3x) + -46080x2 * (-8 + 3x) + 17280x3 * (-8 + 3x) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 ((-8 * -32768 + 3x * -32768) + 61440x * (-8 + 3x) + -46080x2 * (-8 + 3x) + 17280x3 * (-8 + 3x) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 ((262144 + -98304x) + 61440x * (-8 + 3x) + -46080x2 * (-8 + 3x) + 17280x3 * (-8 + 3x) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + (-8 * 61440x + 3x * 61440x) + -46080x2 * (-8 + 3x) + 17280x3 * (-8 + 3x) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + (-491520x + 184320x2) + -46080x2 * (-8 + 3x) + 17280x3 * (-8 + 3x) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + -491520x + 184320x2 + (-8 * -46080x2 + 3x * -46080x2) + 17280x3 * (-8 + 3x) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + -491520x + 184320x2 + (368640x2 + -138240x3) + 17280x3 * (-8 + 3x) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + -491520x + 184320x2 + 368640x2 + -138240x3 + (-8 * 17280x3 + 3x * 17280x3) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + -491520x + 184320x2 + 368640x2 + -138240x3 + (-138240x3 + 51840x4) + -3240x4 * (-8 + 3x) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + -491520x + 184320x2 + 368640x2 + -138240x3 + -138240x3 + 51840x4 + (-8 * -3240x4 + 3x * -3240x4) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + -491520x + 184320x2 + 368640x2 + -138240x3 + -138240x3 + 51840x4 + (25920x4 + -9720x5) + 243x5 * (-8 + 3x)) = 4096 (262144 + -98304x + -491520x + 184320x2 + 368640x2 + -138240x3 + -138240x3 + 51840x4 + 25920x4 + -9720x5 + (-8 * 243x5 + 3x * 243x5)) = 4096 (262144 + -98304x + -491520x + 184320x2 + 368640x2 + -138240x3 + -138240x3 + 51840x4 + 25920x4 + -9720x5 + (-1944x5 + 729x6)) = 4096 Combine like terms: -98304x + -491520x = -589824x (262144 + -589824x + 184320x2 + 368640x2 + -138240x3 + -138240x3 + 51840x4 + 25920x4 + -9720x5 + -1944x5 + 729x6) = 4096 Combine like terms: 184320x2 + 368640x2 = 552960x2 (262144 + -589824x + 552960x2 + -138240x3 + -138240x3 + 51840x4 + 25920x4 + -9720x5 + -1944x5 + 729x6) = 4096 Combine like terms: -138240x3 + -138240x3 = -276480x3 (262144 + -589824x + 552960x2 + -276480x3 + 51840x4 + 25920x4 + -9720x5 + -1944x5 + 729x6) = 4096 Combine like terms: 51840x4 + 25920x4 = 77760x4 (262144 + -589824x + 552960x2 + -276480x3 + 77760x4 + -9720x5 + -1944x5 + 729x6) = 4096 Combine like terms: -9720x5 + -1944x5 = -11664x5 (262144 + -589824x + 552960x2 + -276480x3 + 77760x4 + -11664x5 + 729x6) = 4096 Solving 262144 + -589824x + 552960x2 + -276480x3 + 77760x4 + -11664x5 + 729x6 = 4096 Solving for variable 'x'. Reorder the terms: 262144 + -4096 + -589824x + 552960x2 + -276480x3 + 77760x4 + -11664x5 + 729x6 = 4096 + -4096 Combine like terms: 262144 + -4096 = 258048 258048 + -589824x + 552960x2 + -276480x3 + 77760x4 + -11664x5 + 729x6 = 4096 + -4096 Combine like terms: 4096 + -4096 = 0 258048 + -589824x + 552960x2 + -276480x3 + 77760x4 + -11664x5 + 729x6 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(28672 + -65536x + 61440x2 + -30720x3 + 8640x4 + -1296x5 + 81x6) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(28672 + -65536x + 61440x2 + -30720x3 + 8640x4 + -1296x5 + 81x6)' equal to zero and attempt to solve: Simplifying 28672 + -65536x + 61440x2 + -30720x3 + 8640x4 + -1296x5 + 81x6 = 0 Solving 28672 + -65536x + 61440x2 + -30720x3 + 8640x4 + -1296x5 + 81x6 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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