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Simplifying (2x + -17)(x + -5) + -1(3x + 1)(x + -7) = 84 Reorder the terms: (-17 + 2x)(x + -5) + -1(3x + 1)(x + -7) = 84 Reorder the terms: (-17 + 2x)(-5 + x) + -1(3x + 1)(x + -7) = 84 Multiply (-17 + 2x) * (-5 + x) (-17(-5 + x) + 2x * (-5 + x)) + -1(3x + 1)(x + -7) = 84 ((-5 * -17 + x * -17) + 2x * (-5 + x)) + -1(3x + 1)(x + -7) = 84 ((85 + -17x) + 2x * (-5 + x)) + -1(3x + 1)(x + -7) = 84 (85 + -17x + (-5 * 2x + x * 2x)) + -1(3x + 1)(x + -7) = 84 (85 + -17x + (-10x + 2x2)) + -1(3x + 1)(x + -7) = 84 Combine like terms: -17x + -10x = -27x (85 + -27x + 2x2) + -1(3x + 1)(x + -7) = 84 Reorder the terms: 85 + -27x + 2x2 + -1(1 + 3x)(x + -7) = 84 Reorder the terms: 85 + -27x + 2x2 + -1(1 + 3x)(-7 + x) = 84 Multiply (1 + 3x) * (-7 + x) 85 + -27x + 2x2 + -1(1(-7 + x) + 3x * (-7 + x)) = 84 85 + -27x + 2x2 + -1((-7 * 1 + x * 1) + 3x * (-7 + x)) = 84 85 + -27x + 2x2 + -1((-7 + 1x) + 3x * (-7 + x)) = 84 85 + -27x + 2x2 + -1(-7 + 1x + (-7 * 3x + x * 3x)) = 84 85 + -27x + 2x2 + -1(-7 + 1x + (-21x + 3x2)) = 84 Combine like terms: 1x + -21x = -20x 85 + -27x + 2x2 + -1(-7 + -20x + 3x2) = 84 85 + -27x + 2x2 + (-7 * -1 + -20x * -1 + 3x2 * -1) = 84 85 + -27x + 2x2 + (7 + 20x + -3x2) = 84 Reorder the terms: 85 + 7 + -27x + 20x + 2x2 + -3x2 = 84 Combine like terms: 85 + 7 = 92 92 + -27x + 20x + 2x2 + -3x2 = 84 Combine like terms: -27x + 20x = -7x 92 + -7x + 2x2 + -3x2 = 84 Combine like terms: 2x2 + -3x2 = -1x2 92 + -7x + -1x2 = 84 Solving 92 + -7x + -1x2 = 84 Solving for variable 'x'. Reorder the terms: 92 + -84 + -7x + -1x2 = 84 + -84 Combine like terms: 92 + -84 = 8 8 + -7x + -1x2 = 84 + -84 Combine like terms: 84 + -84 = 0 8 + -7x + -1x2 = 0 Factor a trinomial. (1 + -1x)(8 + x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {1, -8}
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