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Simplifying (x + -7)(4x + -1) + -1(7 + -2x)(x + -7) = 0 Reorder the terms: (-7 + x)(4x + -1) + -1(7 + -2x)(x + -7) = 0 Reorder the terms: (-7 + x)(-1 + 4x) + -1(7 + -2x)(x + -7) = 0 Multiply (-7 + x) * (-1 + 4x) (-7(-1 + 4x) + x(-1 + 4x)) + -1(7 + -2x)(x + -7) = 0 ((-1 * -7 + 4x * -7) + x(-1 + 4x)) + -1(7 + -2x)(x + -7) = 0 ((7 + -28x) + x(-1 + 4x)) + -1(7 + -2x)(x + -7) = 0 (7 + -28x + (-1 * x + 4x * x)) + -1(7 + -2x)(x + -7) = 0 (7 + -28x + (-1x + 4x2)) + -1(7 + -2x)(x + -7) = 0 Combine like terms: -28x + -1x = -29x (7 + -29x + 4x2) + -1(7 + -2x)(x + -7) = 0 Reorder the terms: 7 + -29x + 4x2 + -1(7 + -2x)(-7 + x) = 0 Multiply (7 + -2x) * (-7 + x) 7 + -29x + 4x2 + -1(7(-7 + x) + -2x * (-7 + x)) = 0 7 + -29x + 4x2 + -1((-7 * 7 + x * 7) + -2x * (-7 + x)) = 0 7 + -29x + 4x2 + -1((-49 + 7x) + -2x * (-7 + x)) = 0 7 + -29x + 4x2 + -1(-49 + 7x + (-7 * -2x + x * -2x)) = 0 7 + -29x + 4x2 + -1(-49 + 7x + (14x + -2x2)) = 0 Combine like terms: 7x + 14x = 21x 7 + -29x + 4x2 + -1(-49 + 21x + -2x2) = 0 7 + -29x + 4x2 + (-49 * -1 + 21x * -1 + -2x2 * -1) = 0 7 + -29x + 4x2 + (49 + -21x + 2x2) = 0 Reorder the terms: 7 + 49 + -29x + -21x + 4x2 + 2x2 = 0 Combine like terms: 7 + 49 = 56 56 + -29x + -21x + 4x2 + 2x2 = 0 Combine like terms: -29x + -21x = -50x 56 + -50x + 4x2 + 2x2 = 0 Combine like terms: 4x2 + 2x2 = 6x2 56 + -50x + 6x2 = 0 Solving 56 + -50x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -25x + 3x2) = 0 Factor a trinomial. 2((4 + -3x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1.333333333, 7}
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