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Simplifying x6 + -1 = (x + -10)(x + 1)(x2 + x + 1)(x2 + -1x + 1) Reorder the terms: -1 + x6 = (x + -10)(x + 1)(x2 + x + 1)(x2 + -1x + 1) Reorder the terms: -1 + x6 = (-10 + x)(x + 1)(x2 + x + 1)(x2 + -1x + 1) Reorder the terms: -1 + x6 = (-10 + x)(1 + x)(x2 + x + 1)(x2 + -1x + 1) Reorder the terms: -1 + x6 = (-10 + x)(1 + x)(1 + x + x2)(x2 + -1x + 1) Reorder the terms: -1 + x6 = (-10 + x)(1 + x)(1 + x + x2)(1 + -1x + x2) Multiply (-10 + x) * (1 + x) -1 + x6 = (-10(1 + x) + x(1 + x))(1 + x + x2)(1 + -1x + x2) -1 + x6 = ((1 * -10 + x * -10) + x(1 + x))(1 + x + x2)(1 + -1x + x2) -1 + x6 = ((-10 + -10x) + x(1 + x))(1 + x + x2)(1 + -1x + x2) -1 + x6 = (-10 + -10x + (1 * x + x * x))(1 + x + x2)(1 + -1x + x2) -1 + x6 = (-10 + -10x + (1x + x2))(1 + x + x2)(1 + -1x + x2) Combine like terms: -10x + 1x = -9x -1 + x6 = (-10 + -9x + x2)(1 + x + x2)(1 + -1x + x2) Multiply (-10 + -9x + x2) * (1 + x + x2) -1 + x6 = (-10(1 + x + x2) + -9x * (1 + x + x2) + x2(1 + x + x2))(1 + -1x + x2) -1 + x6 = ((1 * -10 + x * -10 + x2 * -10) + -9x * (1 + x + x2) + x2(1 + x + x2))(1 + -1x + x2) -1 + x6 = ((-10 + -10x + -10x2) + -9x * (1 + x + x2) + x2(1 + x + x2))(1 + -1x + x2) -1 + x6 = (-10 + -10x + -10x2 + (1 * -9x + x * -9x + x2 * -9x) + x2(1 + x + x2))(1 + -1x + x2) -1 + x6 = (-10 + -10x + -10x2 + (-9x + -9x2 + -9x3) + x2(1 + x + x2))(1 + -1x + x2) -1 + x6 = (-10 + -10x + -10x2 + -9x + -9x2 + -9x3 + (1 * x2 + x * x2 + x2 * x2))(1 + -1x + x2) -1 + x6 = (-10 + -10x + -10x2 + -9x + -9x2 + -9x3 + (1x2 + x3 + x4))(1 + -1x + x2) Reorder the terms: -1 + x6 = (-10 + -10x + -9x + -10x2 + -9x2 + 1x2 + -9x3 + x3 + x4)(1 + -1x + x2) Combine like terms: -10x + -9x = -19x -1 + x6 = (-10 + -19x + -10x2 + -9x2 + 1x2 + -9x3 + x3 + x4)(1 + -1x + x2) Combine like terms: -10x2 + -9x2 = -19x2 -1 + x6 = (-10 + -19x + -19x2 + 1x2 + -9x3 + x3 + x4)(1 + -1x + x2) Combine like terms: -19x2 + 1x2 = -18x2 -1 + x6 = (-10 + -19x + -18x2 + -9x3 + x3 + x4)(1 + -1x + x2) Combine like terms: -9x3 + x3 = -8x3 -1 + x6 = (-10 + -19x + -18x2 + -8x3 + x4)(1 + -1x + x2) Multiply (-10 + -19x + -18x2 + -8x3 + x4) * (1 + -1x + x2) -1 + x6 = (-10(1 + -1x + x2) + -19x * (1 + -1x + x2) + -18x2 * (1 + -1x + x2) + -8x3 * (1 + -1x + x2) + x4(1 + -1x + x2)) -1 + x6 = ((1 * -10 + -1x * -10 + x2 * -10) + -19x * (1 + -1x + x2) + -18x2 * (1 + -1x + x2) + -8x3 * (1 + -1x + x2) + x4(1 + -1x + x2)) -1 + x6 = ((-10 + 10x + -10x2) + -19x * (1 + -1x + x2) + -18x2 * (1 + -1x + x2) + -8x3 * (1 + -1x + x2) + x4(1 + -1x + x2)) -1 + x6 = (-10 + 10x + -10x2 + (1 * -19x + -1x * -19x + x2 * -19x) + -18x2 * (1 + -1x + x2) + -8x3 * (1 + -1x + x2) + x4(1 + -1x + x2)) -1 + x6 = (-10 + 10x + -10x2 + (-19x + 19x2 + -19x3) + -18x2 * (1 + -1x + x2) + -8x3 * (1 + -1x + x2) + x4(1 + -1x + x2)) -1 + x6 = (-10 + 10x + -10x2 + -19x + 19x2 + -19x3 + (1 * -18x2 + -1x * -18x2 + x2 * -18x2) + -8x3 * (1 + -1x + x2) + x4(1 + -1x + x2)) -1 + x6 = (-10 + 10x + -10x2 + -19x + 19x2 + -19x3 + (-18x2 + 18x3 + -18x4) + -8x3 * (1 + -1x + x2) + x4(1 + -1x + x2)) -1 + x6 = (-10 + 10x + -10x2 + -19x + 19x2 + -19x3 + -18x2 + 18x3 + -18x4 + (1 * -8x3 + -1x * -8x3 + x2 * -8x3) + x4(1 + -1x + x2)) -1 + x6 = (-10 + 10x + -10x2 + -19x + 19x2 + -19x3 + -18x2 + 18x3 + -18x4 + (-8x3 + 8x4 + -8x5) + x4(1 + -1x + x2)) -1 + x6 = (-10 + 10x + -10x2 + -19x + 19x2 + -19x3 + -18x2 + 18x3 + -18x4 + -8x3 + 8x4 + -8x5 + (1 * x4 + -1x * x4 + x2 * x4)) -1 + x6 = (-10 + 10x + -10x2 + -19x + 19x2 + -19x3 + -18x2 + 18x3 + -18x4 + -8x3 + 8x4 + -8x5 + (1x4 + -1x5 + x6)) Reorder the terms: -1 + x6 = (-10 + 10x + -19x + -10x2 + 19x2 + -18x2 + -19x3 + 18x3 + -8x3 + -18x4 + 8x4 + 1x4 + -8x5 + -1x5 + x6) Combine like terms: 10x + -19x = -9x -1 + x6 = (-10 + -9x + -10x2 + 19x2 + -18x2 + -19x3 + 18x3 + -8x3 + -18x4 + 8x4 + 1x4 + -8x5 + -1x5 + x6) Combine like terms: -10x2 + 19x2 = 9x2 -1 + x6 = (-10 + -9x + 9x2 + -18x2 + -19x3 + 18x3 + -8x3 + -18x4 + 8x4 + 1x4 + -8x5 + -1x5 + x6) Combine like terms: 9x2 + -18x2 = -9x2 -1 + x6 = (-10 + -9x + -9x2 + -19x3 + 18x3 + -8x3 + -18x4 + 8x4 + 1x4 + -8x5 + -1x5 + x6) Combine like terms: -19x3 + 18x3 = -1x3 -1 + x6 = (-10 + -9x + -9x2 + -1x3 + -8x3 + -18x4 + 8x4 + 1x4 + -8x5 + -1x5 + x6) Combine like terms: -1x3 + -8x3 = -9x3 -1 + x6 = (-10 + -9x + -9x2 + -9x3 + -18x4 + 8x4 + 1x4 + -8x5 + -1x5 + x6) Combine like terms: -18x4 + 8x4 = -10x4 -1 + x6 = (-10 + -9x + -9x2 + -9x3 + -10x4 + 1x4 + -8x5 + -1x5 + x6) Combine like terms: -10x4 + 1x4 = -9x4 -1 + x6 = (-10 + -9x + -9x2 + -9x3 + -9x4 + -8x5 + -1x5 + x6) Combine like terms: -8x5 + -1x5 = -9x5 -1 + x6 = (-10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 + x6) Add '-1x6' to each side of the equation. -1 + x6 + -1x6 = -10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 + x6 + -1x6 Combine like terms: x6 + -1x6 = 0 -1 + 0 = -10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 + x6 + -1x6 -1 = -10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 + x6 + -1x6 Combine like terms: x6 + -1x6 = 0 -1 = -10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 + 0 -1 = -10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 Solving -1 = -10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 Solving for variable 'x'. Combine like terms: -1 + 10 = 9 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = -10 + -9x + -9x2 + -9x3 + -9x4 + -9x5 + 10 + 9x + 9x2 + 9x3 + 9x4 + 9x5 Reorder the terms: 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = -10 + 10 + -9x + 9x + -9x2 + 9x2 + -9x3 + 9x3 + -9x4 + 9x4 + -9x5 + 9x5 Combine like terms: -10 + 10 = 0 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = 0 + -9x + 9x + -9x2 + 9x2 + -9x3 + 9x3 + -9x4 + 9x4 + -9x5 + 9x5 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = -9x + 9x + -9x2 + 9x2 + -9x3 + 9x3 + -9x4 + 9x4 + -9x5 + 9x5 Combine like terms: -9x + 9x = 0 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = 0 + -9x2 + 9x2 + -9x3 + 9x3 + -9x4 + 9x4 + -9x5 + 9x5 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = -9x2 + 9x2 + -9x3 + 9x3 + -9x4 + 9x4 + -9x5 + 9x5 Combine like terms: -9x2 + 9x2 = 0 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = 0 + -9x3 + 9x3 + -9x4 + 9x4 + -9x5 + 9x5 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = -9x3 + 9x3 + -9x4 + 9x4 + -9x5 + 9x5 Combine like terms: -9x3 + 9x3 = 0 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = 0 + -9x4 + 9x4 + -9x5 + 9x5 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = -9x4 + 9x4 + -9x5 + 9x5 Combine like terms: -9x4 + 9x4 = 0 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = 0 + -9x5 + 9x5 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = -9x5 + 9x5 Combine like terms: -9x5 + 9x5 = 0 9 + 9x + 9x2 + 9x3 + 9x4 + 9x5 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(1 + x + x2 + x3 + x4 + x5) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + x + x2 + x3 + x4 + x5)' equal to zero and attempt to solve: Simplifying 1 + x + x2 + x3 + x4 + x5 = 0 Solving 1 + x + x2 + x3 + x4 + x5 = 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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