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Simplifying (5x + 2)(1 + -2x) + -1(6x + 2)(5x + 2) = 0 Reorder the terms: (2 + 5x)(1 + -2x) + -1(6x + 2)(5x + 2) = 0 Multiply (2 + 5x) * (1 + -2x) (2(1 + -2x) + 5x * (1 + -2x)) + -1(6x + 2)(5x + 2) = 0 ((1 * 2 + -2x * 2) + 5x * (1 + -2x)) + -1(6x + 2)(5x + 2) = 0 ((2 + -4x) + 5x * (1 + -2x)) + -1(6x + 2)(5x + 2) = 0 (2 + -4x + (1 * 5x + -2x * 5x)) + -1(6x + 2)(5x + 2) = 0 (2 + -4x + (5x + -10x2)) + -1(6x + 2)(5x + 2) = 0 Combine like terms: -4x + 5x = 1x (2 + 1x + -10x2) + -1(6x + 2)(5x + 2) = 0 Reorder the terms: 2 + 1x + -10x2 + -1(2 + 6x)(5x + 2) = 0 Reorder the terms: 2 + 1x + -10x2 + -1(2 + 6x)(2 + 5x) = 0 Multiply (2 + 6x) * (2 + 5x) 2 + 1x + -10x2 + -1(2(2 + 5x) + 6x * (2 + 5x)) = 0 2 + 1x + -10x2 + -1((2 * 2 + 5x * 2) + 6x * (2 + 5x)) = 0 2 + 1x + -10x2 + -1((4 + 10x) + 6x * (2 + 5x)) = 0 2 + 1x + -10x2 + -1(4 + 10x + (2 * 6x + 5x * 6x)) = 0 2 + 1x + -10x2 + -1(4 + 10x + (12x + 30x2)) = 0 Combine like terms: 10x + 12x = 22x 2 + 1x + -10x2 + -1(4 + 22x + 30x2) = 0 2 + 1x + -10x2 + (4 * -1 + 22x * -1 + 30x2 * -1) = 0 2 + 1x + -10x2 + (-4 + -22x + -30x2) = 0 Reorder the terms: 2 + -4 + 1x + -22x + -10x2 + -30x2 = 0 Combine like terms: 2 + -4 = -2 -2 + 1x + -22x + -10x2 + -30x2 = 0 Combine like terms: 1x + -22x = -21x -2 + -21x + -10x2 + -30x2 = 0 Combine like terms: -10x2 + -30x2 = -40x2 -2 + -21x + -40x2 = 0 Solving -2 + -21x + -40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 21x + 40x2) = 0 Factor a trinomial. -1((2 + 5x)(1 + 8x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve: Simplifying 1 + 8x = 0 Solving 1 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x = 0 + -1 8x = 0 + -1 Combine like terms: 0 + -1 = -1 8x = -1 Divide each side by '8'. x = -0.125 Simplifying x = -0.125Solution
x = {-0.4, -0.125}
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