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Simplifying (x + 3)(x + 3)(x + 3)(x + 3) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Reorder the terms: (3 + x)(x + 3)(x + 3)(x + 3) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Reorder the terms: (3 + x)(3 + x)(x + 3)(x + 3) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Reorder the terms: (3 + x)(3 + x)(3 + x)(x + 3) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Reorder the terms: (3 + x)(3 + x)(3 + x)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x))(3 + x)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 ((3 * 3 + x * 3) + x(3 + x))(3 + x)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 ((9 + 3x) + x(3 + x))(3 + x)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (9 + 3x + (3 * x + x * x))(3 + x)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (9 + 3x + (3x + x2))(3 + x)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Combine like terms: 3x + 3x = 6x (9 + 6x + x2)(3 + x)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Multiply (9 + 6x + x2) * (3 + x) (9(3 + x) + 6x * (3 + x) + x2(3 + x))(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 ((3 * 9 + x * 9) + 6x * (3 + x) + x2(3 + x))(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 ((27 + 9x) + 6x * (3 + x) + x2(3 + x))(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (27 + 9x + (3 * 6x + x * 6x) + x2(3 + x))(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (27 + 9x + (18x + 6x2) + x2(3 + x))(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (27 + 9x + 18x + 6x2 + (3 * x2 + x * x2))(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (27 + 9x + 18x + 6x2 + (3x2 + x3))(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Combine like terms: 9x + 18x = 27x (27 + 27x + 6x2 + 3x2 + x3)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Combine like terms: 6x2 + 3x2 = 9x2 (27 + 27x + 9x2 + x3)(3 + x) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Multiply (27 + 27x + 9x2 + x3) * (3 + x) (27(3 + x) + 27x * (3 + x) + 9x2 * (3 + x) + x3(3 + x)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 ((3 * 27 + x * 27) + 27x * (3 + x) + 9x2 * (3 + x) + x3(3 + x)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 ((81 + 27x) + 27x * (3 + x) + 9x2 * (3 + x) + x3(3 + x)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (81 + 27x + (3 * 27x + x * 27x) + 9x2 * (3 + x) + x3(3 + x)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (81 + 27x + (81x + 27x2) + 9x2 * (3 + x) + x3(3 + x)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (81 + 27x + 81x + 27x2 + (3 * 9x2 + x * 9x2) + x3(3 + x)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (81 + 27x + 81x + 27x2 + (27x2 + 9x3) + x3(3 + x)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (81 + 27x + 81x + 27x2 + 27x2 + 9x3 + (3 * x3 + x * x3)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 (81 + 27x + 81x + 27x2 + 27x2 + 9x3 + (3x3 + x4)) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Combine like terms: 27x + 81x = 108x (81 + 108x + 27x2 + 27x2 + 9x3 + 3x3 + x4) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Combine like terms: 27x2 + 27x2 = 54x2 (81 + 108x + 54x2 + 9x3 + 3x3 + x4) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Combine like terms: 9x3 + 3x3 = 12x3 (81 + 108x + 54x2 + 12x3 + x4) + (x + 5)(x + 5)(x + 5)(x + 5) = 16 Reorder the terms: 81 + 108x + 54x2 + 12x3 + x4 + (5 + x)(x + 5)(x + 5)(x + 5) = 16 Reorder the terms: 81 + 108x + 54x2 + 12x3 + x4 + (5 + x)(5 + x)(x + 5)(x + 5) = 16 Reorder the terms: 81 + 108x + 54x2 + 12x3 + x4 + (5 + x)(5 + x)(5 + x)(x + 5) = 16 Reorder the terms: 81 + 108x + 54x2 + 12x3 + x4 + (5 + x)(5 + x)(5 + x)(5 + x) = 16 Multiply (5 + x) * (5 + x) 81 + 108x + 54x2 + 12x3 + x4 + (5(5 + x) + x(5 + x))(5 + x)(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + ((5 * 5 + x * 5) + x(5 + x))(5 + x)(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + ((25 + 5x) + x(5 + x))(5 + x)(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + (25 + 5x + (5 * x + x * x))(5 + x)(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + (25 + 5x + (5x + x2))(5 + x)(5 + x) = 16 Combine like terms: 5x + 5x = 10x 81 + 108x + 54x2 + 12x3 + x4 + (25 + 10x + x2)(5 + x)(5 + x) = 16 Multiply (25 + 10x + x2) * (5 + x) 81 + 108x + 54x2 + 12x3 + x4 + (25(5 + x) + 10x * (5 + x) + x2(5 + x))(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + ((5 * 25 + x * 25) + 10x * (5 + x) + x2(5 + x))(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + ((125 + 25x) + 10x * (5 + x) + x2(5 + x))(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + (125 + 25x + (5 * 10x + x * 10x) + x2(5 + x))(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + (125 + 25x + (50x + 10x2) + x2(5 + x))(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + (125 + 25x + 50x + 10x2 + (5 * x2 + x * x2))(5 + x) = 16 81 + 108x + 54x2 + 12x3 + x4 + (125 + 25x + 50x + 10x2 + (5x2 + x3))(5 + x) = 16 Combine like terms: 25x + 50x = 75x 81 + 108x + 54x2 + 12x3 + x4 + (125 + 75x + 10x2 + 5x2 + x3)(5 + x) = 16 Combine like terms: 10x2 + 5x2 = 15x2 81 + 108x + 54x2 + 12x3 + x4 + (125 + 75x + 15x2 + x3)(5 + x) = 16 Multiply (125 + 75x + 15x2 + x3) * (5 + x) 81 + 108x + 54x2 + 12x3 + x4 + (125(5 + x) + 75x * (5 + x) + 15x2 * (5 + x) + x3(5 + x)) = 16 81 + 108x + 54x2 + 12x3 + x4 + ((5 * 125 + x * 125) + 75x * (5 + x) + 15x2 * (5 + x) + x3(5 + x)) = 16 81 + 108x + 54x2 + 12x3 + x4 + ((625 + 125x) + 75x * (5 + x) + 15x2 * (5 + x) + x3(5 + x)) = 16 81 + 108x + 54x2 + 12x3 + x4 + (625 + 125x + (5 * 75x + x * 75x) + 15x2 * (5 + x) + x3(5 + x)) = 16 81 + 108x + 54x2 + 12x3 + x4 + (625 + 125x + (375x + 75x2) + 15x2 * (5 + x) + x3(5 + x)) = 16 81 + 108x + 54x2 + 12x3 + x4 + (625 + 125x + 375x + 75x2 + (5 * 15x2 + x * 15x2) + x3(5 + x)) = 16 81 + 108x + 54x2 + 12x3 + x4 + (625 + 125x + 375x + 75x2 + (75x2 + 15x3) + x3(5 + x)) = 16 81 + 108x + 54x2 + 12x3 + x4 + (625 + 125x + 375x + 75x2 + 75x2 + 15x3 + (5 * x3 + x * x3)) = 16 81 + 108x + 54x2 + 12x3 + x4 + (625 + 125x + 375x + 75x2 + 75x2 + 15x3 + (5x3 + x4)) = 16 Combine like terms: 125x + 375x = 500x 81 + 108x + 54x2 + 12x3 + x4 + (625 + 500x + 75x2 + 75x2 + 15x3 + 5x3 + x4) = 16 Combine like terms: 75x2 + 75x2 = 150x2 81 + 108x + 54x2 + 12x3 + x4 + (625 + 500x + 150x2 + 15x3 + 5x3 + x4) = 16 Combine like terms: 15x3 + 5x3 = 20x3 81 + 108x + 54x2 + 12x3 + x4 + (625 + 500x + 150x2 + 20x3 + x4) = 16 Reorder the terms: 81 + 625 + 108x + 500x + 54x2 + 150x2 + 12x3 + 20x3 + x4 + x4 = 16 Combine like terms: 81 + 625 = 706 706 + 108x + 500x + 54x2 + 150x2 + 12x3 + 20x3 + x4 + x4 = 16 Combine like terms: 108x + 500x = 608x 706 + 608x + 54x2 + 150x2 + 12x3 + 20x3 + x4 + x4 = 16 Combine like terms: 54x2 + 150x2 = 204x2 706 + 608x + 204x2 + 12x3 + 20x3 + x4 + x4 = 16 Combine like terms: 12x3 + 20x3 = 32x3 706 + 608x + 204x2 + 32x3 + x4 + x4 = 16 Combine like terms: x4 + x4 = 2x4 706 + 608x + 204x2 + 32x3 + 2x4 = 16 Solving 706 + 608x + 204x2 + 32x3 + 2x4 = 16 Solving for variable 'x'. Reorder the terms: 706 + -16 + 608x + 204x2 + 32x3 + 2x4 = 16 + -16 Combine like terms: 706 + -16 = 690 690 + 608x + 204x2 + 32x3 + 2x4 = 16 + -16 Combine like terms: 16 + -16 = 0 690 + 608x + 204x2 + 32x3 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(345 + 304x + 102x2 + 16x3 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(345 + 304x + 102x2 + 16x3 + x4)' equal to zero and attempt to solve: Simplifying 345 + 304x + 102x2 + 16x3 + x4 = 0 Solving 345 + 304x + 102x2 + 16x3 + x4 = 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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