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Simplifying 9(5x + -1)(5x + -1)(5x + -1)(5x + -1) + 5(5x + -1)(5x + -1) + -4 = 0 Reorder the terms: 9(-1 + 5x)(5x + -1)(5x + -1)(5x + -1) + 5(5x + -1)(5x + -1) + -4 = 0 Reorder the terms: 9(-1 + 5x)(-1 + 5x)(5x + -1)(5x + -1) + 5(5x + -1)(5x + -1) + -4 = 0 Reorder the terms: 9(-1 + 5x)(-1 + 5x)(-1 + 5x)(5x + -1) + 5(5x + -1)(5x + -1) + -4 = 0 Reorder the terms: 9(-1 + 5x)(-1 + 5x)(-1 + 5x)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 Multiply (-1 + 5x) * (-1 + 5x) 9(-1(-1 + 5x) + 5x * (-1 + 5x))(-1 + 5x)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9((-1 * -1 + 5x * -1) + 5x * (-1 + 5x))(-1 + 5x)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9((1 + -5x) + 5x * (-1 + 5x))(-1 + 5x)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + (-1 * 5x + 5x * 5x))(-1 + 5x)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + (-5x + 25x2))(-1 + 5x)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 Combine like terms: -5x + -5x = -10x 9(1 + -10x + 25x2)(-1 + 5x)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 Multiply (1 + -10x + 25x2) * (-1 + 5x) 9(1(-1 + 5x) + -10x * (-1 + 5x) + 25x2 * (-1 + 5x))(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9((-1 * 1 + 5x * 1) + -10x * (-1 + 5x) + 25x2 * (-1 + 5x))(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9((-1 + 5x) + -10x * (-1 + 5x) + 25x2 * (-1 + 5x))(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9(-1 + 5x + (-1 * -10x + 5x * -10x) + 25x2 * (-1 + 5x))(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9(-1 + 5x + (10x + -50x2) + 25x2 * (-1 + 5x))(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9(-1 + 5x + 10x + -50x2 + (-1 * 25x2 + 5x * 25x2))(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 9(-1 + 5x + 10x + -50x2 + (-25x2 + 125x3))(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 Combine like terms: 5x + 10x = 15x 9(-1 + 15x + -50x2 + -25x2 + 125x3)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 Combine like terms: -50x2 + -25x2 = -75x2 9(-1 + 15x + -75x2 + 125x3)(-1 + 5x) + 5(5x + -1)(5x + -1) + -4 = 0 Multiply (-1 + 15x + -75x2 + 125x3) * (-1 + 5x) 9(-1(-1 + 5x) + 15x * (-1 + 5x) + -75x2 * (-1 + 5x) + 125x3 * (-1 + 5x)) + 5(5x + -1)(5x + -1) + -4 = 0 9((-1 * -1 + 5x * -1) + 15x * (-1 + 5x) + -75x2 * (-1 + 5x) + 125x3 * (-1 + 5x)) + 5(5x + -1)(5x + -1) + -4 = 0 9((1 + -5x) + 15x * (-1 + 5x) + -75x2 * (-1 + 5x) + 125x3 * (-1 + 5x)) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + (-1 * 15x + 5x * 15x) + -75x2 * (-1 + 5x) + 125x3 * (-1 + 5x)) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + (-15x + 75x2) + -75x2 * (-1 + 5x) + 125x3 * (-1 + 5x)) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + -15x + 75x2 + (-1 * -75x2 + 5x * -75x2) + 125x3 * (-1 + 5x)) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + -15x + 75x2 + (75x2 + -375x3) + 125x3 * (-1 + 5x)) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + -15x + 75x2 + 75x2 + -375x3 + (-1 * 125x3 + 5x * 125x3)) + 5(5x + -1)(5x + -1) + -4 = 0 9(1 + -5x + -15x + 75x2 + 75x2 + -375x3 + (-125x3 + 625x4)) + 5(5x + -1)(5x + -1) + -4 = 0 Combine like terms: -5x + -15x = -20x 9(1 + -20x + 75x2 + 75x2 + -375x3 + -125x3 + 625x4) + 5(5x + -1)(5x + -1) + -4 = 0 Combine like terms: 75x2 + 75x2 = 150x2 9(1 + -20x + 150x2 + -375x3 + -125x3 + 625x4) + 5(5x + -1)(5x + -1) + -4 = 0 Combine like terms: -375x3 + -125x3 = -500x3 9(1 + -20x + 150x2 + -500x3 + 625x4) + 5(5x + -1)(5x + -1) + -4 = 0 (1 * 9 + -20x * 9 + 150x2 * 9 + -500x3 * 9 + 625x4 * 9) + 5(5x + -1)(5x + -1) + -4 = 0 (9 + -180x + 1350x2 + -4500x3 + 5625x4) + 5(5x + -1)(5x + -1) + -4 = 0 Reorder the terms: 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5(-1 + 5x)(5x + -1) + -4 = 0 Reorder the terms: 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5(-1 + 5x)(-1 + 5x) + -4 = 0 Multiply (-1 + 5x) * (-1 + 5x) 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5(-1(-1 + 5x) + 5x * (-1 + 5x)) + -4 = 0 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) + -4 = 0 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5((1 + -5x) + 5x * (-1 + 5x)) + -4 = 0 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5(1 + -5x + (-1 * 5x + 5x * 5x)) + -4 = 0 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5(1 + -5x + (-5x + 25x2)) + -4 = 0 Combine like terms: -5x + -5x = -10x 9 + -180x + 1350x2 + -4500x3 + 5625x4 + 5(1 + -10x + 25x2) + -4 = 0 9 + -180x + 1350x2 + -4500x3 + 5625x4 + (1 * 5 + -10x * 5 + 25x2 * 5) + -4 = 0 9 + -180x + 1350x2 + -4500x3 + 5625x4 + (5 + -50x + 125x2) + -4 = 0 Reorder the terms: 9 + 5 + -4 + -180x + -50x + 1350x2 + 125x2 + -4500x3 + 5625x4 = 0 Combine like terms: 9 + 5 = 14 14 + -4 + -180x + -50x + 1350x2 + 125x2 + -4500x3 + 5625x4 = 0 Combine like terms: 14 + -4 = 10 10 + -180x + -50x + 1350x2 + 125x2 + -4500x3 + 5625x4 = 0 Combine like terms: -180x + -50x = -230x 10 + -230x + 1350x2 + 125x2 + -4500x3 + 5625x4 = 0 Combine like terms: 1350x2 + 125x2 = 1475x2 10 + -230x + 1475x2 + -4500x3 + 5625x4 = 0 Solving 10 + -230x + 1475x2 + -4500x3 + 5625x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -46x + 295x2 + -900x3 + 1125x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -46x + 295x2 + -900x3 + 1125x4)' equal to zero and attempt to solve: Simplifying 2 + -46x + 295x2 + -900x3 + 1125x4 = 0 Solving 2 + -46x + 295x2 + -900x3 + 1125x4 = 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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