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Simplifying (x + 1)(3x + 1) = (2x)(14 + -3x) + (x + 1) Reorder the terms: (1 + x)(3x + 1) = (2x)(14 + -3x) + (x + 1) Reorder the terms: (1 + x)(1 + 3x) = (2x)(14 + -3x) + (x + 1) Multiply (1 + x) * (1 + 3x) (1(1 + 3x) + x(1 + 3x)) = (2x)(14 + -3x) + (x + 1) ((1 * 1 + 3x * 1) + x(1 + 3x)) = (2x)(14 + -3x) + (x + 1) ((1 + 3x) + x(1 + 3x)) = (2x)(14 + -3x) + (x + 1) (1 + 3x + (1 * x + 3x * x)) = (2x)(14 + -3x) + (x + 1) (1 + 3x + (1x + 3x2)) = (2x)(14 + -3x) + (x + 1) Combine like terms: 3x + 1x = 4x (1 + 4x + 3x2) = (2x)(14 + -3x) + (x + 1) Remove parenthesis around (2x) 1 + 4x + 3x2 = 2x(14 + -3x) + (x + 1) 1 + 4x + 3x2 = (14 * 2x + -3x * 2x) + (x + 1) 1 + 4x + 3x2 = (28x + -6x2) + (x + 1) Reorder the terms: 1 + 4x + 3x2 = 28x + -6x2 + (1 + x) Remove parenthesis around (1 + x) 1 + 4x + 3x2 = 28x + -6x2 + 1 + x Reorder the terms: 1 + 4x + 3x2 = 1 + 28x + x + -6x2 Combine like terms: 28x + x = 29x 1 + 4x + 3x2 = 1 + 29x + -6x2 Add '-1' to each side of the equation. 1 + 4x + -1 + 3x2 = 1 + 29x + -1 + -6x2 Reorder the terms: 1 + -1 + 4x + 3x2 = 1 + 29x + -1 + -6x2 Combine like terms: 1 + -1 = 0 0 + 4x + 3x2 = 1 + 29x + -1 + -6x2 4x + 3x2 = 1 + 29x + -1 + -6x2 Reorder the terms: 4x + 3x2 = 1 + -1 + 29x + -6x2 Combine like terms: 1 + -1 = 0 4x + 3x2 = 0 + 29x + -6x2 4x + 3x2 = 29x + -6x2 Solving 4x + 3x2 = 29x + -6x2 Solving for variable 'x'. Reorder the terms: 4x + -29x + 3x2 + 6x2 = 29x + -6x2 + -29x + 6x2 Combine like terms: 4x + -29x = -25x -25x + 3x2 + 6x2 = 29x + -6x2 + -29x + 6x2 Combine like terms: 3x2 + 6x2 = 9x2 -25x + 9x2 = 29x + -6x2 + -29x + 6x2 Reorder the terms: -25x + 9x2 = 29x + -29x + -6x2 + 6x2 Combine like terms: 29x + -29x = 0 -25x + 9x2 = 0 + -6x2 + 6x2 -25x + 9x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -25x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-25 + 9x) = 0Subproblem 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 '(-25 + 9x)' equal to zero and attempt to solve: Simplifying -25 + 9x = 0 Solving -25 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 9x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 9x = 0 + 25 9x = 0 + 25 Combine like terms: 0 + 25 = 25 9x = 25 Divide each side by '9'. x = 2.777777778 Simplifying x = 2.777777778Solution
x = {0, 2.777777778}
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