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Simplifying (x + -5)(4x + -1) + 2(2 + -8x)(x + -5) = 0 Reorder the terms: (-5 + x)(4x + -1) + 2(2 + -8x)(x + -5) = 0 Reorder the terms: (-5 + x)(-1 + 4x) + 2(2 + -8x)(x + -5) = 0 Multiply (-5 + x) * (-1 + 4x) (-5(-1 + 4x) + x(-1 + 4x)) + 2(2 + -8x)(x + -5) = 0 ((-1 * -5 + 4x * -5) + x(-1 + 4x)) + 2(2 + -8x)(x + -5) = 0 ((5 + -20x) + x(-1 + 4x)) + 2(2 + -8x)(x + -5) = 0 (5 + -20x + (-1 * x + 4x * x)) + 2(2 + -8x)(x + -5) = 0 (5 + -20x + (-1x + 4x2)) + 2(2 + -8x)(x + -5) = 0 Combine like terms: -20x + -1x = -21x (5 + -21x + 4x2) + 2(2 + -8x)(x + -5) = 0 Reorder the terms: 5 + -21x + 4x2 + 2(2 + -8x)(-5 + x) = 0 Multiply (2 + -8x) * (-5 + x) 5 + -21x + 4x2 + 2(2(-5 + x) + -8x * (-5 + x)) = 0 5 + -21x + 4x2 + 2((-5 * 2 + x * 2) + -8x * (-5 + x)) = 0 5 + -21x + 4x2 + 2((-10 + 2x) + -8x * (-5 + x)) = 0 5 + -21x + 4x2 + 2(-10 + 2x + (-5 * -8x + x * -8x)) = 0 5 + -21x + 4x2 + 2(-10 + 2x + (40x + -8x2)) = 0 Combine like terms: 2x + 40x = 42x 5 + -21x + 4x2 + 2(-10 + 42x + -8x2) = 0 5 + -21x + 4x2 + (-10 * 2 + 42x * 2 + -8x2 * 2) = 0 5 + -21x + 4x2 + (-20 + 84x + -16x2) = 0 Reorder the terms: 5 + -20 + -21x + 84x + 4x2 + -16x2 = 0 Combine like terms: 5 + -20 = -15 -15 + -21x + 84x + 4x2 + -16x2 = 0 Combine like terms: -21x + 84x = 63x -15 + 63x + 4x2 + -16x2 = 0 Combine like terms: 4x2 + -16x2 = -12x2 -15 + 63x + -12x2 = 0 Solving -15 + 63x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 21x + -4x2) = 0 Factor a trinomial. 3((-5 + x)(1 + -4x)) = 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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {5, 0.25}
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