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Simplifying 1120 = (x + 3)(x + 4)(5 + x)(6 + x)(7 + x) Reorder the terms: 1120 = (3 + x)(x + 4)(5 + x)(6 + x)(7 + x) Reorder the terms: 1120 = (3 + x)(4 + x)(5 + x)(6 + x)(7 + x) Multiply (3 + x) * (4 + x) 1120 = (3(4 + x) + x(4 + x))(5 + x)(6 + x)(7 + x) 1120 = ((4 * 3 + x * 3) + x(4 + x))(5 + x)(6 + x)(7 + x) 1120 = ((12 + 3x) + x(4 + x))(5 + x)(6 + x)(7 + x) 1120 = (12 + 3x + (4 * x + x * x))(5 + x)(6 + x)(7 + x) 1120 = (12 + 3x + (4x + x2))(5 + x)(6 + x)(7 + x) Combine like terms: 3x + 4x = 7x 1120 = (12 + 7x + x2)(5 + x)(6 + x)(7 + x) Multiply (12 + 7x + x2) * (5 + x) 1120 = (12(5 + x) + 7x * (5 + x) + x2(5 + x))(6 + x)(7 + x) 1120 = ((5 * 12 + x * 12) + 7x * (5 + x) + x2(5 + x))(6 + x)(7 + x) 1120 = ((60 + 12x) + 7x * (5 + x) + x2(5 + x))(6 + x)(7 + x) 1120 = (60 + 12x + (5 * 7x + x * 7x) + x2(5 + x))(6 + x)(7 + x) 1120 = (60 + 12x + (35x + 7x2) + x2(5 + x))(6 + x)(7 + x) 1120 = (60 + 12x + 35x + 7x2 + (5 * x2 + x * x2))(6 + x)(7 + x) 1120 = (60 + 12x + 35x + 7x2 + (5x2 + x3))(6 + x)(7 + x) Combine like terms: 12x + 35x = 47x 1120 = (60 + 47x + 7x2 + 5x2 + x3)(6 + x)(7 + x) Combine like terms: 7x2 + 5x2 = 12x2 1120 = (60 + 47x + 12x2 + x3)(6 + x)(7 + x) Multiply (60 + 47x + 12x2 + x3) * (6 + x) 1120 = (60(6 + x) + 47x * (6 + x) + 12x2 * (6 + x) + x3(6 + x))(7 + x) 1120 = ((6 * 60 + x * 60) + 47x * (6 + x) + 12x2 * (6 + x) + x3(6 + x))(7 + x) 1120 = ((360 + 60x) + 47x * (6 + x) + 12x2 * (6 + x) + x3(6 + x))(7 + x) 1120 = (360 + 60x + (6 * 47x + x * 47x) + 12x2 * (6 + x) + x3(6 + x))(7 + x) 1120 = (360 + 60x + (282x + 47x2) + 12x2 * (6 + x) + x3(6 + x))(7 + x) 1120 = (360 + 60x + 282x + 47x2 + (6 * 12x2 + x * 12x2) + x3(6 + x))(7 + x) 1120 = (360 + 60x + 282x + 47x2 + (72x2 + 12x3) + x3(6 + x))(7 + x) 1120 = (360 + 60x + 282x + 47x2 + 72x2 + 12x3 + (6 * x3 + x * x3))(7 + x) 1120 = (360 + 60x + 282x + 47x2 + 72x2 + 12x3 + (6x3 + x4))(7 + x) Combine like terms: 60x + 282x = 342x 1120 = (360 + 342x + 47x2 + 72x2 + 12x3 + 6x3 + x4)(7 + x) Combine like terms: 47x2 + 72x2 = 119x2 1120 = (360 + 342x + 119x2 + 12x3 + 6x3 + x4)(7 + x) Combine like terms: 12x3 + 6x3 = 18x3 1120 = (360 + 342x + 119x2 + 18x3 + x4)(7 + x) Multiply (360 + 342x + 119x2 + 18x3 + x4) * (7 + x) 1120 = (360(7 + x) + 342x * (7 + x) + 119x2 * (7 + x) + 18x3 * (7 + x) + x4(7 + x)) 1120 = ((7 * 360 + x * 360) + 342x * (7 + x) + 119x2 * (7 + x) + 18x3 * (7 + x) + x4(7 + x)) 1120 = ((2520 + 360x) + 342x * (7 + x) + 119x2 * (7 + x) + 18x3 * (7 + x) + x4(7 + x)) 1120 = (2520 + 360x + (7 * 342x + x * 342x) + 119x2 * (7 + x) + 18x3 * (7 + x) + x4(7 + x)) 1120 = (2520 + 360x + (2394x + 342x2) + 119x2 * (7 + x) + 18x3 * (7 + x) + x4(7 + x)) 1120 = (2520 + 360x + 2394x + 342x2 + (7 * 119x2 + x * 119x2) + 18x3 * (7 + x) + x4(7 + x)) 1120 = (2520 + 360x + 2394x + 342x2 + (833x2 + 119x3) + 18x3 * (7 + x) + x4(7 + x)) 1120 = (2520 + 360x + 2394x + 342x2 + 833x2 + 119x3 + (7 * 18x3 + x * 18x3) + x4(7 + x)) 1120 = (2520 + 360x + 2394x + 342x2 + 833x2 + 119x3 + (126x3 + 18x4) + x4(7 + x)) 1120 = (2520 + 360x + 2394x + 342x2 + 833x2 + 119x3 + 126x3 + 18x4 + (7 * x4 + x * x4)) 1120 = (2520 + 360x + 2394x + 342x2 + 833x2 + 119x3 + 126x3 + 18x4 + (7x4 + x5)) Combine like terms: 360x + 2394x = 2754x 1120 = (2520 + 2754x + 342x2 + 833x2 + 119x3 + 126x3 + 18x4 + 7x4 + x5) Combine like terms: 342x2 + 833x2 = 1175x2 1120 = (2520 + 2754x + 1175x2 + 119x3 + 126x3 + 18x4 + 7x4 + x5) Combine like terms: 119x3 + 126x3 = 245x3 1120 = (2520 + 2754x + 1175x2 + 245x3 + 18x4 + 7x4 + x5) Combine like terms: 18x4 + 7x4 = 25x4 1120 = (2520 + 2754x + 1175x2 + 245x3 + 25x4 + x5) Solving 1120 = 2520 + 2754x + 1175x2 + 245x3 + 25x4 + x5 Solving for variable 'x'. Combine like terms: 1120 + -2520 = -1400 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 2520 + 2754x + 1175x2 + 245x3 + 25x4 + x5 + -2520 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 Reorder the terms: -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 2520 + -2520 + 2754x + -2754x + 1175x2 + -1175x2 + 245x3 + -245x3 + 25x4 + -25x4 + x5 + -1x5 Combine like terms: 2520 + -2520 = 0 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 0 + 2754x + -2754x + 1175x2 + -1175x2 + 245x3 + -245x3 + 25x4 + -25x4 + x5 + -1x5 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 2754x + -2754x + 1175x2 + -1175x2 + 245x3 + -245x3 + 25x4 + -25x4 + x5 + -1x5 Combine like terms: 2754x + -2754x = 0 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 0 + 1175x2 + -1175x2 + 245x3 + -245x3 + 25x4 + -25x4 + x5 + -1x5 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 1175x2 + -1175x2 + 245x3 + -245x3 + 25x4 + -25x4 + x5 + -1x5 Combine like terms: 1175x2 + -1175x2 = 0 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 0 + 245x3 + -245x3 + 25x4 + -25x4 + x5 + -1x5 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 245x3 + -245x3 + 25x4 + -25x4 + x5 + -1x5 Combine like terms: 245x3 + -245x3 = 0 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 0 + 25x4 + -25x4 + x5 + -1x5 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 25x4 + -25x4 + x5 + -1x5 Combine like terms: 25x4 + -25x4 = 0 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 0 + x5 + -1x5 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = x5 + -1x5 Combine like terms: x5 + -1x5 = 0 -1400 + -2754x + -1175x2 + -245x3 + -25x4 + -1x5 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1400 + 2754x + 1175x2 + 245x3 + 25x4 + x5) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1400 + 2754x + 1175x2 + 245x3 + 25x4 + x5)' equal to zero and attempt to solve: Simplifying 1400 + 2754x + 1175x2 + 245x3 + 25x4 + x5 = 0 Solving 1400 + 2754x + 1175x2 + 245x3 + 25x4 + 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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