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Simplifying 88888(x + 8)(x + 16) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) Reorder the terms: 88888(8 + x)(x + 16) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) Reorder the terms: 88888(8 + x)(16 + x) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) Multiply (8 + x) * (16 + x) 88888(8(16 + x) + x(16 + x)) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) 88888((16 * 8 + x * 8) + x(16 + x)) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) 88888((128 + 8x) + x(16 + x)) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) 88888(128 + 8x + (16 * x + x * x)) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) 88888(128 + 8x + (16x + x2)) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) Combine like terms: 8x + 16x = 24x 88888(128 + 24x + x2) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) (128 * 88888 + 24x * 88888 + x2 * 88888) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) (11377664 + 2133312x + 88888x2) + 44444(x + 12)(x + 8) = 66666(x + 4)(x + 8) Reorder the terms: 11377664 + 2133312x + 88888x2 + 44444(12 + x)(x + 8) = 66666(x + 4)(x + 8) Reorder the terms: 11377664 + 2133312x + 88888x2 + 44444(12 + x)(8 + x) = 66666(x + 4)(x + 8) Multiply (12 + x) * (8 + x) 11377664 + 2133312x + 88888x2 + 44444(12(8 + x) + x(8 + x)) = 66666(x + 4)(x + 8) 11377664 + 2133312x + 88888x2 + 44444((8 * 12 + x * 12) + x(8 + x)) = 66666(x + 4)(x + 8) 11377664 + 2133312x + 88888x2 + 44444((96 + 12x) + x(8 + x)) = 66666(x + 4)(x + 8) 11377664 + 2133312x + 88888x2 + 44444(96 + 12x + (8 * x + x * x)) = 66666(x + 4)(x + 8) 11377664 + 2133312x + 88888x2 + 44444(96 + 12x + (8x + x2)) = 66666(x + 4)(x + 8) Combine like terms: 12x + 8x = 20x 11377664 + 2133312x + 88888x2 + 44444(96 + 20x + x2) = 66666(x + 4)(x + 8) 11377664 + 2133312x + 88888x2 + (96 * 44444 + 20x * 44444 + x2 * 44444) = 66666(x + 4)(x + 8) 11377664 + 2133312x + 88888x2 + (4266624 + 888880x + 44444x2) = 66666(x + 4)(x + 8) Reorder the terms: 11377664 + 4266624 + 2133312x + 888880x + 88888x2 + 44444x2 = 66666(x + 4)(x + 8) Combine like terms: 11377664 + 4266624 = 15644288 15644288 + 2133312x + 888880x + 88888x2 + 44444x2 = 66666(x + 4)(x + 8) Combine like terms: 2133312x + 888880x = 3022192x 15644288 + 3022192x + 88888x2 + 44444x2 = 66666(x + 4)(x + 8) Combine like terms: 88888x2 + 44444x2 = 133332x2 15644288 + 3022192x + 133332x2 = 66666(x + 4)(x + 8) Reorder the terms: 15644288 + 3022192x + 133332x2 = 66666(4 + x)(x + 8) Reorder the terms: 15644288 + 3022192x + 133332x2 = 66666(4 + x)(8 + x) Multiply (4 + x) * (8 + x) 15644288 + 3022192x + 133332x2 = 66666(4(8 + x) + x(8 + x)) 15644288 + 3022192x + 133332x2 = 66666((8 * 4 + x * 4) + x(8 + x)) 15644288 + 3022192x + 133332x2 = 66666((32 + 4x) + x(8 + x)) 15644288 + 3022192x + 133332x2 = 66666(32 + 4x + (8 * x + x * x)) 15644288 + 3022192x + 133332x2 = 66666(32 + 4x + (8x + x2)) Combine like terms: 4x + 8x = 12x 15644288 + 3022192x + 133332x2 = 66666(32 + 12x + x2) 15644288 + 3022192x + 133332x2 = (32 * 66666 + 12x * 66666 + x2 * 66666) 15644288 + 3022192x + 133332x2 = (2133312 + 799992x + 66666x2) Solving 15644288 + 3022192x + 133332x2 = 2133312 + 799992x + 66666x2 Solving for variable 'x'. Reorder the terms: 15644288 + -2133312 + 3022192x + -799992x + 133332x2 + -66666x2 = 2133312 + 799992x + 66666x2 + -2133312 + -799992x + -66666x2 Combine like terms: 15644288 + -2133312 = 13510976 13510976 + 3022192x + -799992x + 133332x2 + -66666x2 = 2133312 + 799992x + 66666x2 + -2133312 + -799992x + -66666x2 Combine like terms: 3022192x + -799992x = 2222200x 13510976 + 2222200x + 133332x2 + -66666x2 = 2133312 + 799992x + 66666x2 + -2133312 + -799992x + -66666x2 Combine like terms: 133332x2 + -66666x2 = 66666x2 13510976 + 2222200x + 66666x2 = 2133312 + 799992x + 66666x2 + -2133312 + -799992x + -66666x2 Reorder the terms: 13510976 + 2222200x + 66666x2 = 2133312 + -2133312 + 799992x + -799992x + 66666x2 + -66666x2 Combine like terms: 2133312 + -2133312 = 0 13510976 + 2222200x + 66666x2 = 0 + 799992x + -799992x + 66666x2 + -66666x2 13510976 + 2222200x + 66666x2 = 799992x + -799992x + 66666x2 + -66666x2 Combine like terms: 799992x + -799992x = 0 13510976 + 2222200x + 66666x2 = 0 + 66666x2 + -66666x2 13510976 + 2222200x + 66666x2 = 66666x2 + -66666x2 Combine like terms: 66666x2 + -66666x2 = 0 13510976 + 2222200x + 66666x2 = 0 Factor out the Greatest Common Factor (GCF), '22222'. 22222(608 + 100x + 3x2) = 0 Factor a trinomial. 22222((76 + 3x)(8 + x)) = 0 Ignore the factor 22222.Subproblem 1
Set the factor '(76 + 3x)' equal to zero and attempt to solve: Simplifying 76 + 3x = 0 Solving 76 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-76' to each side of the equation. 76 + -76 + 3x = 0 + -76 Combine like terms: 76 + -76 = 0 0 + 3x = 0 + -76 3x = 0 + -76 Combine like terms: 0 + -76 = -76 3x = -76 Divide each side by '3'. x = -25.33333333 Simplifying x = -25.33333333Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {-25.33333333, -8}
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