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Simplifying (x + 2)(5x + 1) + -1(x + 2)(3x + 2) = 0 Reorder the terms: (2 + x)(5x + 1) + -1(x + 2)(3x + 2) = 0 Reorder the terms: (2 + x)(1 + 5x) + -1(x + 2)(3x + 2) = 0 Multiply (2 + x) * (1 + 5x) (2(1 + 5x) + x(1 + 5x)) + -1(x + 2)(3x + 2) = 0 ((1 * 2 + 5x * 2) + x(1 + 5x)) + -1(x + 2)(3x + 2) = 0 ((2 + 10x) + x(1 + 5x)) + -1(x + 2)(3x + 2) = 0 (2 + 10x + (1 * x + 5x * x)) + -1(x + 2)(3x + 2) = 0 (2 + 10x + (1x + 5x2)) + -1(x + 2)(3x + 2) = 0 Combine like terms: 10x + 1x = 11x (2 + 11x + 5x2) + -1(x + 2)(3x + 2) = 0 Reorder the terms: 2 + 11x + 5x2 + -1(2 + x)(3x + 2) = 0 Reorder the terms: 2 + 11x + 5x2 + -1(2 + x)(2 + 3x) = 0 Multiply (2 + x) * (2 + 3x) 2 + 11x + 5x2 + -1(2(2 + 3x) + x(2 + 3x)) = 0 2 + 11x + 5x2 + -1((2 * 2 + 3x * 2) + x(2 + 3x)) = 0 2 + 11x + 5x2 + -1((4 + 6x) + x(2 + 3x)) = 0 2 + 11x + 5x2 + -1(4 + 6x + (2 * x + 3x * x)) = 0 2 + 11x + 5x2 + -1(4 + 6x + (2x + 3x2)) = 0 Combine like terms: 6x + 2x = 8x 2 + 11x + 5x2 + -1(4 + 8x + 3x2) = 0 2 + 11x + 5x2 + (4 * -1 + 8x * -1 + 3x2 * -1) = 0 2 + 11x + 5x2 + (-4 + -8x + -3x2) = 0 Reorder the terms: 2 + -4 + 11x + -8x + 5x2 + -3x2 = 0 Combine like terms: 2 + -4 = -2 -2 + 11x + -8x + 5x2 + -3x2 = 0 Combine like terms: 11x + -8x = 3x -2 + 3x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 -2 + 3x + 2x2 = 0 Solving -2 + 3x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-2 + -1x)(1 + -2x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-2, 0.5}
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