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Simplifying (-7x + -6)(x + -5) + (8x + -9)(5 + -1x) = 0 Reorder the terms: (-6 + -7x)(x + -5) + (8x + -9)(5 + -1x) = 0 Reorder the terms: (-6 + -7x)(-5 + x) + (8x + -9)(5 + -1x) = 0 Multiply (-6 + -7x) * (-5 + x) (-6(-5 + x) + -7x * (-5 + x)) + (8x + -9)(5 + -1x) = 0 ((-5 * -6 + x * -6) + -7x * (-5 + x)) + (8x + -9)(5 + -1x) = 0 ((30 + -6x) + -7x * (-5 + x)) + (8x + -9)(5 + -1x) = 0 (30 + -6x + (-5 * -7x + x * -7x)) + (8x + -9)(5 + -1x) = 0 (30 + -6x + (35x + -7x2)) + (8x + -9)(5 + -1x) = 0 Combine like terms: -6x + 35x = 29x (30 + 29x + -7x2) + (8x + -9)(5 + -1x) = 0 Reorder the terms: 30 + 29x + -7x2 + (-9 + 8x)(5 + -1x) = 0 Multiply (-9 + 8x) * (5 + -1x) 30 + 29x + -7x2 + (-9(5 + -1x) + 8x * (5 + -1x)) = 0 30 + 29x + -7x2 + ((5 * -9 + -1x * -9) + 8x * (5 + -1x)) = 0 30 + 29x + -7x2 + ((-45 + 9x) + 8x * (5 + -1x)) = 0 30 + 29x + -7x2 + (-45 + 9x + (5 * 8x + -1x * 8x)) = 0 30 + 29x + -7x2 + (-45 + 9x + (40x + -8x2)) = 0 Combine like terms: 9x + 40x = 49x 30 + 29x + -7x2 + (-45 + 49x + -8x2) = 0 Reorder the terms: 30 + -45 + 29x + 49x + -7x2 + -8x2 = 0 Combine like terms: 30 + -45 = -15 -15 + 29x + 49x + -7x2 + -8x2 = 0 Combine like terms: 29x + 49x = 78x -15 + 78x + -7x2 + -8x2 = 0 Combine like terms: -7x2 + -8x2 = -15x2 -15 + 78x + -15x2 = 0 Solving -15 + 78x + -15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 26x + -5x2) = 0 Factor a trinomial. 3((-5 + x)(1 + -5x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {5, 0.2}
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