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Simplifying (2 + 3x)(3 + 4x)(4 + 5x) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Multiply (2 + 3x) * (3 + 4x) (2(3 + 4x) + 3x * (3 + 4x))(4 + 5x) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 ((3 * 2 + 4x * 2) + 3x * (3 + 4x))(4 + 5x) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 ((6 + 8x) + 3x * (3 + 4x))(4 + 5x) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 (6 + 8x + (3 * 3x + 4x * 3x))(4 + 5x) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 (6 + 8x + (9x + 12x2))(4 + 5x) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 8x + 9x = 17x (6 + 17x + 12x2)(4 + 5x) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Multiply (6 + 17x + 12x2) * (4 + 5x) (6(4 + 5x) + 17x * (4 + 5x) + 12x2 * (4 + 5x)) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 ((4 * 6 + 5x * 6) + 17x * (4 + 5x) + 12x2 * (4 + 5x)) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 ((24 + 30x) + 17x * (4 + 5x) + 12x2 * (4 + 5x)) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 (24 + 30x + (4 * 17x + 5x * 17x) + 12x2 * (4 + 5x)) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 (24 + 30x + (68x + 85x2) + 12x2 * (4 + 5x)) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 (24 + 30x + 68x + 85x2 + (4 * 12x2 + 5x * 12x2)) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 (24 + 30x + 68x + 85x2 + (48x2 + 60x3)) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 30x + 68x = 98x (24 + 98x + 85x2 + 48x2 + 60x3) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 85x2 + 48x2 = 133x2 (24 + 98x + 133x2 + 60x3) + -2(1 + 2x)(3 + 4x)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Multiply (1 + 2x) * (3 + 4x) 24 + 98x + 133x2 + 60x3 + -2(1(3 + 4x) + 2x * (3 + 4x))(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2((3 * 1 + 4x * 1) + 2x * (3 + 4x))(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2((3 + 4x) + 2x * (3 + 4x))(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2(3 + 4x + (3 * 2x + 4x * 2x))(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2(3 + 4x + (6x + 8x2))(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 4x + 6x = 10x 24 + 98x + 133x2 + 60x3 + -2(3 + 10x + 8x2)(4 + 5x) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Multiply (3 + 10x + 8x2) * (4 + 5x) 24 + 98x + 133x2 + 60x3 + -2(3(4 + 5x) + 10x * (4 + 5x) + 8x2 * (4 + 5x)) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2((4 * 3 + 5x * 3) + 10x * (4 + 5x) + 8x2 * (4 + 5x)) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2((12 + 15x) + 10x * (4 + 5x) + 8x2 * (4 + 5x)) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2(12 + 15x + (4 * 10x + 5x * 10x) + 8x2 * (4 + 5x)) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2(12 + 15x + (40x + 50x2) + 8x2 * (4 + 5x)) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2(12 + 15x + 40x + 50x2 + (4 * 8x2 + 5x * 8x2)) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -2(12 + 15x + 40x + 50x2 + (32x2 + 40x3)) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 15x + 40x = 55x 24 + 98x + 133x2 + 60x3 + -2(12 + 55x + 50x2 + 32x2 + 40x3) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 50x2 + 32x2 = 82x2 24 + 98x + 133x2 + 60x3 + -2(12 + 55x + 82x2 + 40x3) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + (12 * -2 + 55x * -2 + 82x2 * -2 + 40x3 * -2) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + (-24 + -110x + -164x2 + -80x3) + 3(1 + 2x)(2 + 3x)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Multiply (1 + 2x) * (2 + 3x) 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(1(2 + 3x) + 2x * (2 + 3x))(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3((2 * 1 + 3x * 1) + 2x * (2 + 3x))(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3((2 + 3x) + 2x * (2 + 3x))(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(2 + 3x + (2 * 2x + 3x * 2x))(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(2 + 3x + (4x + 6x2))(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 3x + 4x = 7x 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(2 + 7x + 6x2)(4 + 5x) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Multiply (2 + 7x + 6x2) * (4 + 5x) 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(2(4 + 5x) + 7x * (4 + 5x) + 6x2 * (4 + 5x)) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3((4 * 2 + 5x * 2) + 7x * (4 + 5x) + 6x2 * (4 + 5x)) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3((8 + 10x) + 7x * (4 + 5x) + 6x2 * (4 + 5x)) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(8 + 10x + (4 * 7x + 5x * 7x) + 6x2 * (4 + 5x)) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(8 + 10x + (28x + 35x2) + 6x2 * (4 + 5x)) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(8 + 10x + 28x + 35x2 + (4 * 6x2 + 5x * 6x2)) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(8 + 10x + 28x + 35x2 + (24x2 + 30x3)) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 10x + 28x = 38x 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(8 + 38x + 35x2 + 24x2 + 30x3) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Combine like terms: 35x2 + 24x2 = 59x2 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 3(8 + 38x + 59x2 + 30x3) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + (8 * 3 + 38x * 3 + 59x2 * 3 + 30x3 * 3) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + (24 + 114x + 177x2 + 90x3) + -4(1 + 2x)(2 + 3x)(3 + 4x) = 0 Multiply (1 + 2x) * (2 + 3x) 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(1(2 + 3x) + 2x * (2 + 3x))(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4((2 * 1 + 3x * 1) + 2x * (2 + 3x))(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4((2 + 3x) + 2x * (2 + 3x))(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(2 + 3x + (2 * 2x + 3x * 2x))(3 + 4x) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(2 + 3x + (4x + 6x2))(3 + 4x) = 0 Combine like terms: 3x + 4x = 7x 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(2 + 7x + 6x2)(3 + 4x) = 0 Multiply (2 + 7x + 6x2) * (3 + 4x) 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(2(3 + 4x) + 7x * (3 + 4x) + 6x2 * (3 + 4x)) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4((3 * 2 + 4x * 2) + 7x * (3 + 4x) + 6x2 * (3 + 4x)) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4((6 + 8x) + 7x * (3 + 4x) + 6x2 * (3 + 4x)) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(6 + 8x + (3 * 7x + 4x * 7x) + 6x2 * (3 + 4x)) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(6 + 8x + (21x + 28x2) + 6x2 * (3 + 4x)) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(6 + 8x + 21x + 28x2 + (3 * 6x2 + 4x * 6x2)) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(6 + 8x + 21x + 28x2 + (18x2 + 24x3)) = 0 Combine like terms: 8x + 21x = 29x 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(6 + 29x + 28x2 + 18x2 + 24x3) = 0 Combine like terms: 28x2 + 18x2 = 46x2 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + -4(6 + 29x + 46x2 + 24x3) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + (6 * -4 + 29x * -4 + 46x2 * -4 + 24x3 * -4) = 0 24 + 98x + 133x2 + 60x3 + -24 + -110x + -164x2 + -80x3 + 24 + 114x + 177x2 + 90x3 + (-24 + -116x + -184x2 + -96x3) = 0 Reorder the terms: 24 + -24 + 24 + -24 + 98x + -110x + 114x + -116x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: 24 + -24 = 0 0 + 24 + -24 + 98x + -110x + 114x + -116x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 24 + -24 + 98x + -110x + 114x + -116x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: 24 + -24 = 0 0 + 98x + -110x + 114x + -116x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 98x + -110x + 114x + -116x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: 98x + -110x = -12x -12x + 114x + -116x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: -12x + 114x = 102x 102x + -116x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: 102x + -116x = -14x -14x + 133x2 + -164x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: 133x2 + -164x2 = -31x2 -14x + -31x2 + 177x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: -31x2 + 177x2 = 146x2 -14x + 146x2 + -184x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: 146x2 + -184x2 = -38x2 -14x + -38x2 + 60x3 + -80x3 + 90x3 + -96x3 = 0 Combine like terms: 60x3 + -80x3 = -20x3 -14x + -38x2 + -20x3 + 90x3 + -96x3 = 0 Combine like terms: -20x3 + 90x3 = 70x3 -14x + -38x2 + 70x3 + -96x3 = 0 Combine like terms: 70x3 + -96x3 = -26x3 -14x + -38x2 + -26x3 = 0 Solving -14x + -38x2 + -26x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2x'. -2x(7 + 19x + 13x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + 19x + 13x2)' equal to zero and attempt to solve: Simplifying 7 + 19x + 13x2 = 0 Solving 7 + 19x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.5384615385 + 1.461538462x + x2 = 0 Move the constant term to the right: Add '-0.5384615385' to each side of the equation. 0.5384615385 + 1.461538462x + -0.5384615385 + x2 = 0 + -0.5384615385 Reorder the terms: 0.5384615385 + -0.5384615385 + 1.461538462x + x2 = 0 + -0.5384615385 Combine like terms: 0.5384615385 + -0.5384615385 = 0.0000000000 0.0000000000 + 1.461538462x + x2 = 0 + -0.5384615385 1.461538462x + x2 = 0 + -0.5384615385 Combine like terms: 0 + -0.5384615385 = -0.5384615385 1.461538462x + x2 = -0.5384615385 The x term is 1.461538462x. Take half its coefficient (0.730769231). Square it (0.5340236690) and add it to both sides. Add '0.5340236690' to each side of the equation. 1.461538462x + 0.5340236690 + x2 = -0.5384615385 + 0.5340236690 Reorder the terms: 0.5340236690 + 1.461538462x + x2 = -0.5384615385 + 0.5340236690 Combine like terms: -0.5384615385 + 0.5340236690 = -0.0044378695 0.5340236690 + 1.461538462x + x2 = -0.0044378695 Factor a perfect square on the left side: (x + 0.730769231)(x + 0.730769231) = -0.0044378695 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
| b+18=46 | | 1(4)(5)+8(1)(7)= | | n-2=103 | | 15x^2-7x-4= | | 2x+1+3x-8=x-3 | | n+12=45 | | 2x+x=39 | | -17(1)(6)= | | u^2-34u+102=0 | | x-6.6=-1.8 | | y=-5x^2+15x+50 | | x-19=30 | | 15x^2-14x-8= | | n+13=22 | | a^2-34a+102=0 | | 20x^2-7x-6= | | (8x-x)-(7x+3x)= | | 12x-1=23 | | 2x+7=44 | | a^2-34a+96=0 | | 3(2x-1)=9(x+2)-5 | | a^2-30a+150=0 | | 4x-5=2x-5 | | 5x+1= | | 7x^2y+8xy^2+y^3= | | U=G(1+rt) | | y+8+3=14 | | y=fx+s | | z^2+2z+10= | | 3x-7=3x+7 | | 6x^2-13x+5= | | 2z+5-7z=21-7z |