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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 = 19x (-5 + 19x + 4x2) + 2(2 + -8x)(x + -5) = 0 Reorder the terms: -5 + 19x + 4x2 + 2(2 + -8x)(-5 + x) = 0 Multiply (2 + -8x) * (-5 + x) -5 + 19x + 4x2 + 2(2(-5 + x) + -8x * (-5 + x)) = 0 -5 + 19x + 4x2 + 2((-5 * 2 + x * 2) + -8x * (-5 + x)) = 0 -5 + 19x + 4x2 + 2((-10 + 2x) + -8x * (-5 + x)) = 0 -5 + 19x + 4x2 + 2(-10 + 2x + (-5 * -8x + x * -8x)) = 0 -5 + 19x + 4x2 + 2(-10 + 2x + (40x + -8x2)) = 0 Combine like terms: 2x + 40x = 42x -5 + 19x + 4x2 + 2(-10 + 42x + -8x2) = 0 -5 + 19x + 4x2 + (-10 * 2 + 42x * 2 + -8x2 * 2) = 0 -5 + 19x + 4x2 + (-20 + 84x + -16x2) = 0 Reorder the terms: -5 + -20 + 19x + 84x + 4x2 + -16x2 = 0 Combine like terms: -5 + -20 = -25 -25 + 19x + 84x + 4x2 + -16x2 = 0 Combine like terms: 19x + 84x = 103x -25 + 103x + 4x2 + -16x2 = 0 Combine like terms: 4x2 + -16x2 = -12x2 -25 + 103x + -12x2 = 0 Solving -25 + 103x + -12x2 = 0 Solving for variable 'x'. Factor a trinomial. (-25 + 3x)(1 + -4x) = 0Subproblem 1
Set the factor '(-25 + 3x)' equal to zero and attempt to solve: Simplifying -25 + 3x = 0 Solving -25 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 3x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 3x = 0 + 25 3x = 0 + 25 Combine like terms: 0 + 25 = 25 3x = 25 Divide each side by '3'. x = 8.333333333 Simplifying x = 8.333333333Subproblem 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 = {8.333333333, 0.25}
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