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Simplifying (x + -6)(x + -5) + (x + -7)(x + -4) = 10 Reorder the terms: (-6 + x)(x + -5) + (x + -7)(x + -4) = 10 Reorder the terms: (-6 + x)(-5 + x) + (x + -7)(x + -4) = 10 Multiply (-6 + x) * (-5 + x) (-6(-5 + x) + x(-5 + x)) + (x + -7)(x + -4) = 10 ((-5 * -6 + x * -6) + x(-5 + x)) + (x + -7)(x + -4) = 10 ((30 + -6x) + x(-5 + x)) + (x + -7)(x + -4) = 10 (30 + -6x + (-5 * x + x * x)) + (x + -7)(x + -4) = 10 (30 + -6x + (-5x + x2)) + (x + -7)(x + -4) = 10 Combine like terms: -6x + -5x = -11x (30 + -11x + x2) + (x + -7)(x + -4) = 10 Reorder the terms: 30 + -11x + x2 + (-7 + x)(x + -4) = 10 Reorder the terms: 30 + -11x + x2 + (-7 + x)(-4 + x) = 10 Multiply (-7 + x) * (-4 + x) 30 + -11x + x2 + (-7(-4 + x) + x(-4 + x)) = 10 30 + -11x + x2 + ((-4 * -7 + x * -7) + x(-4 + x)) = 10 30 + -11x + x2 + ((28 + -7x) + x(-4 + x)) = 10 30 + -11x + x2 + (28 + -7x + (-4 * x + x * x)) = 10 30 + -11x + x2 + (28 + -7x + (-4x + x2)) = 10 Combine like terms: -7x + -4x = -11x 30 + -11x + x2 + (28 + -11x + x2) = 10 Reorder the terms: 30 + 28 + -11x + -11x + x2 + x2 = 10 Combine like terms: 30 + 28 = 58 58 + -11x + -11x + x2 + x2 = 10 Combine like terms: -11x + -11x = -22x 58 + -22x + x2 + x2 = 10 Combine like terms: x2 + x2 = 2x2 58 + -22x + 2x2 = 10 Solving 58 + -22x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: 58 + -10 + -22x + 2x2 = 10 + -10 Combine like terms: 58 + -10 = 48 48 + -22x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 48 + -22x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -11x + x2) = 0 Factor a trinomial. 2((3 + -1x)(8 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {3, 8}
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