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Simplifying (5x + 7)(x + -5) = -2x(2x + 5) + x + -31 Reorder the terms: (7 + 5x)(x + -5) = -2x(2x + 5) + x + -31 Reorder the terms: (7 + 5x)(-5 + x) = -2x(2x + 5) + x + -31 Multiply (7 + 5x) * (-5 + x) (7(-5 + x) + 5x * (-5 + x)) = -2x(2x + 5) + x + -31 ((-5 * 7 + x * 7) + 5x * (-5 + x)) = -2x(2x + 5) + x + -31 ((-35 + 7x) + 5x * (-5 + x)) = -2x(2x + 5) + x + -31 (-35 + 7x + (-5 * 5x + x * 5x)) = -2x(2x + 5) + x + -31 (-35 + 7x + (-25x + 5x2)) = -2x(2x + 5) + x + -31 Combine like terms: 7x + -25x = -18x (-35 + -18x + 5x2) = -2x(2x + 5) + x + -31 Reorder the terms: -35 + -18x + 5x2 = -2x(5 + 2x) + x + -31 -35 + -18x + 5x2 = (5 * -2x + 2x * -2x) + x + -31 -35 + -18x + 5x2 = (-10x + -4x2) + x + -31 Reorder the terms: -35 + -18x + 5x2 = -31 + -10x + x + -4x2 Combine like terms: -10x + x = -9x -35 + -18x + 5x2 = -31 + -9x + -4x2 Solving -35 + -18x + 5x2 = -31 + -9x + -4x2 Solving for variable 'x'. Reorder the terms: -35 + 31 + -18x + 9x + 5x2 + 4x2 = -31 + -9x + -4x2 + 31 + 9x + 4x2 Combine like terms: -35 + 31 = -4 -4 + -18x + 9x + 5x2 + 4x2 = -31 + -9x + -4x2 + 31 + 9x + 4x2 Combine like terms: -18x + 9x = -9x -4 + -9x + 5x2 + 4x2 = -31 + -9x + -4x2 + 31 + 9x + 4x2 Combine like terms: 5x2 + 4x2 = 9x2 -4 + -9x + 9x2 = -31 + -9x + -4x2 + 31 + 9x + 4x2 Reorder the terms: -4 + -9x + 9x2 = -31 + 31 + -9x + 9x + -4x2 + 4x2 Combine like terms: -31 + 31 = 0 -4 + -9x + 9x2 = 0 + -9x + 9x + -4x2 + 4x2 -4 + -9x + 9x2 = -9x + 9x + -4x2 + 4x2 Combine like terms: -9x + 9x = 0 -4 + -9x + 9x2 = 0 + -4x2 + 4x2 -4 + -9x + 9x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -4 + -9x + 9x2 = 0 Factor a trinomial. (-1 + -3x)(4 + -3x) = 0Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
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 = 1.333333333Solution
x = {-0.3333333333, 1.333333333}
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