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Simplifying (5x + 7)(5x + -7) + -1(5x + 7)(2x + 6) = 0 Reorder the terms: (7 + 5x)(5x + -7) + -1(5x + 7)(2x + 6) = 0 Reorder the terms: (7 + 5x)(-7 + 5x) + -1(5x + 7)(2x + 6) = 0 Multiply (7 + 5x) * (-7 + 5x) (7(-7 + 5x) + 5x * (-7 + 5x)) + -1(5x + 7)(2x + 6) = 0 ((-7 * 7 + 5x * 7) + 5x * (-7 + 5x)) + -1(5x + 7)(2x + 6) = 0 ((-49 + 35x) + 5x * (-7 + 5x)) + -1(5x + 7)(2x + 6) = 0 (-49 + 35x + (-7 * 5x + 5x * 5x)) + -1(5x + 7)(2x + 6) = 0 (-49 + 35x + (-35x + 25x2)) + -1(5x + 7)(2x + 6) = 0 Combine like terms: 35x + -35x = 0 (-49 + 0 + 25x2) + -1(5x + 7)(2x + 6) = 0 (-49 + 25x2) + -1(5x + 7)(2x + 6) = 0 Reorder the terms: -49 + 25x2 + -1(7 + 5x)(2x + 6) = 0 Reorder the terms: -49 + 25x2 + -1(7 + 5x)(6 + 2x) = 0 Multiply (7 + 5x) * (6 + 2x) -49 + 25x2 + -1(7(6 + 2x) + 5x * (6 + 2x)) = 0 -49 + 25x2 + -1((6 * 7 + 2x * 7) + 5x * (6 + 2x)) = 0 -49 + 25x2 + -1((42 + 14x) + 5x * (6 + 2x)) = 0 -49 + 25x2 + -1(42 + 14x + (6 * 5x + 2x * 5x)) = 0 -49 + 25x2 + -1(42 + 14x + (30x + 10x2)) = 0 Combine like terms: 14x + 30x = 44x -49 + 25x2 + -1(42 + 44x + 10x2) = 0 -49 + 25x2 + (42 * -1 + 44x * -1 + 10x2 * -1) = 0 -49 + 25x2 + (-42 + -44x + -10x2) = 0 Reorder the terms: -49 + -42 + -44x + 25x2 + -10x2 = 0 Combine like terms: -49 + -42 = -91 -91 + -44x + 25x2 + -10x2 = 0 Combine like terms: 25x2 + -10x2 = 15x2 -91 + -44x + 15x2 = 0 Solving -91 + -44x + 15x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -5x)(13 + -3x) = 0Subproblem 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 '(13 + -3x)' equal to zero and attempt to solve: Simplifying 13 + -3x = 0 Solving 13 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3x = 0 + -13 -3x = 0 + -13 Combine like terms: 0 + -13 = -13 -3x = -13 Divide each side by '-3'. x = 4.333333333 Simplifying x = 4.333333333Solution
x = {-1.4, 4.333333333}
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