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Simplifying (5x + -7) + -1(3x + 4)(7 + -5x) = 25x2 + -49 Reorder the terms: (-7 + 5x) + -1(3x + 4)(7 + -5x) = 25x2 + -49 Remove parenthesis around (-7 + 5x) -7 + 5x + -1(3x + 4)(7 + -5x) = 25x2 + -49 Reorder the terms: -7 + 5x + -1(4 + 3x)(7 + -5x) = 25x2 + -49 Multiply (4 + 3x) * (7 + -5x) -7 + 5x + -1(4(7 + -5x) + 3x * (7 + -5x)) = 25x2 + -49 -7 + 5x + -1((7 * 4 + -5x * 4) + 3x * (7 + -5x)) = 25x2 + -49 -7 + 5x + -1((28 + -20x) + 3x * (7 + -5x)) = 25x2 + -49 -7 + 5x + -1(28 + -20x + (7 * 3x + -5x * 3x)) = 25x2 + -49 -7 + 5x + -1(28 + -20x + (21x + -15x2)) = 25x2 + -49 Combine like terms: -20x + 21x = 1x -7 + 5x + -1(28 + 1x + -15x2) = 25x2 + -49 -7 + 5x + (28 * -1 + 1x * -1 + -15x2 * -1) = 25x2 + -49 -7 + 5x + (-28 + -1x + 15x2) = 25x2 + -49 Reorder the terms: -7 + -28 + 5x + -1x + 15x2 = 25x2 + -49 Combine like terms: -7 + -28 = -35 -35 + 5x + -1x + 15x2 = 25x2 + -49 Combine like terms: 5x + -1x = 4x -35 + 4x + 15x2 = 25x2 + -49 Reorder the terms: -35 + 4x + 15x2 = -49 + 25x2 Solving -35 + 4x + 15x2 = -49 + 25x2 Solving for variable 'x'. Reorder the terms: -35 + 49 + 4x + 15x2 + -25x2 = -49 + 25x2 + 49 + -25x2 Combine like terms: -35 + 49 = 14 14 + 4x + 15x2 + -25x2 = -49 + 25x2 + 49 + -25x2 Combine like terms: 15x2 + -25x2 = -10x2 14 + 4x + -10x2 = -49 + 25x2 + 49 + -25x2 Reorder the terms: 14 + 4x + -10x2 = -49 + 49 + 25x2 + -25x2 Combine like terms: -49 + 49 = 0 14 + 4x + -10x2 = 0 + 25x2 + -25x2 14 + 4x + -10x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 14 + 4x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 2x + -5x2) = 0 Factor a trinomial. 2((7 + -5x)(1 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 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 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {1.4, -1}
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