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Simplifying (x + -2)(x + -5) + (x + -2)(3x + -1) = 0 Reorder the terms: (-2 + x)(x + -5) + (x + -2)(3x + -1) = 0 Reorder the terms: (-2 + x)(-5 + x) + (x + -2)(3x + -1) = 0 Multiply (-2 + x) * (-5 + x) (-2(-5 + x) + x(-5 + x)) + (x + -2)(3x + -1) = 0 ((-5 * -2 + x * -2) + x(-5 + x)) + (x + -2)(3x + -1) = 0 ((10 + -2x) + x(-5 + x)) + (x + -2)(3x + -1) = 0 (10 + -2x + (-5 * x + x * x)) + (x + -2)(3x + -1) = 0 (10 + -2x + (-5x + x2)) + (x + -2)(3x + -1) = 0 Combine like terms: -2x + -5x = -7x (10 + -7x + x2) + (x + -2)(3x + -1) = 0 Reorder the terms: 10 + -7x + x2 + (-2 + x)(3x + -1) = 0 Reorder the terms: 10 + -7x + x2 + (-2 + x)(-1 + 3x) = 0 Multiply (-2 + x) * (-1 + 3x) 10 + -7x + x2 + (-2(-1 + 3x) + x(-1 + 3x)) = 0 10 + -7x + x2 + ((-1 * -2 + 3x * -2) + x(-1 + 3x)) = 0 10 + -7x + x2 + ((2 + -6x) + x(-1 + 3x)) = 0 10 + -7x + x2 + (2 + -6x + (-1 * x + 3x * x)) = 0 10 + -7x + x2 + (2 + -6x + (-1x + 3x2)) = 0 Combine like terms: -6x + -1x = -7x 10 + -7x + x2 + (2 + -7x + 3x2) = 0 Reorder the terms: 10 + 2 + -7x + -7x + x2 + 3x2 = 0 Combine like terms: 10 + 2 = 12 12 + -7x + -7x + x2 + 3x2 = 0 Combine like terms: -7x + -7x = -14x 12 + -14x + x2 + 3x2 = 0 Combine like terms: x2 + 3x2 = 4x2 12 + -14x + 4x2 = 0 Solving 12 + -14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -7x + 2x2) = 0 Factor a trinomial. 2((3 + -2x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
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 = 2Solution
x = {1.5, 2}
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