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Simplifying (10x + 9)(2x + -6) + -1(5x + -7)(2x + -7) = 8 Reorder the terms: (9 + 10x)(2x + -6) + -1(5x + -7)(2x + -7) = 8 Reorder the terms: (9 + 10x)(-6 + 2x) + -1(5x + -7)(2x + -7) = 8 Multiply (9 + 10x) * (-6 + 2x) (9(-6 + 2x) + 10x * (-6 + 2x)) + -1(5x + -7)(2x + -7) = 8 ((-6 * 9 + 2x * 9) + 10x * (-6 + 2x)) + -1(5x + -7)(2x + -7) = 8 ((-54 + 18x) + 10x * (-6 + 2x)) + -1(5x + -7)(2x + -7) = 8 (-54 + 18x + (-6 * 10x + 2x * 10x)) + -1(5x + -7)(2x + -7) = 8 (-54 + 18x + (-60x + 20x2)) + -1(5x + -7)(2x + -7) = 8 Combine like terms: 18x + -60x = -42x (-54 + -42x + 20x2) + -1(5x + -7)(2x + -7) = 8 Reorder the terms: -54 + -42x + 20x2 + -1(-7 + 5x)(2x + -7) = 8 Reorder the terms: -54 + -42x + 20x2 + -1(-7 + 5x)(-7 + 2x) = 8 Multiply (-7 + 5x) * (-7 + 2x) -54 + -42x + 20x2 + -1(-7(-7 + 2x) + 5x * (-7 + 2x)) = 8 -54 + -42x + 20x2 + -1((-7 * -7 + 2x * -7) + 5x * (-7 + 2x)) = 8 -54 + -42x + 20x2 + -1((49 + -14x) + 5x * (-7 + 2x)) = 8 -54 + -42x + 20x2 + -1(49 + -14x + (-7 * 5x + 2x * 5x)) = 8 -54 + -42x + 20x2 + -1(49 + -14x + (-35x + 10x2)) = 8 Combine like terms: -14x + -35x = -49x -54 + -42x + 20x2 + -1(49 + -49x + 10x2) = 8 -54 + -42x + 20x2 + (49 * -1 + -49x * -1 + 10x2 * -1) = 8 -54 + -42x + 20x2 + (-49 + 49x + -10x2) = 8 Reorder the terms: -54 + -49 + -42x + 49x + 20x2 + -10x2 = 8 Combine like terms: -54 + -49 = -103 -103 + -42x + 49x + 20x2 + -10x2 = 8 Combine like terms: -42x + 49x = 7x -103 + 7x + 20x2 + -10x2 = 8 Combine like terms: 20x2 + -10x2 = 10x2 -103 + 7x + 10x2 = 8 Solving -103 + 7x + 10x2 = 8 Solving for variable 'x'. Reorder the terms: -103 + -8 + 7x + 10x2 = 8 + -8 Combine like terms: -103 + -8 = -111 -111 + 7x + 10x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -111 + 7x + 10x2 = 0 Factor a trinomial. (-37 + -10x)(3 + -1x) = 0Subproblem 1
Set the factor '(-37 + -10x)' equal to zero and attempt to solve: Simplifying -37 + -10x = 0 Solving -37 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + -10x = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -10x = 0 + 37 -10x = 0 + 37 Combine like terms: 0 + 37 = 37 -10x = 37 Divide each side by '-10'. x = -3.7 Simplifying x = -3.7Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3.7, 3}
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