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Simplifying 8[5 + -1(4 + -5x)] + 5x = 5x(9x + 5) + -17 8[5 + (4 * -1 + -5x * -1)] + 5x = 5x(9x + 5) + -17 8[5 + (-4 + 5x)] + 5x = 5x(9x + 5) + -17 Combine like terms: 5 + -4 = 1 8[1 + 5x] + 5x = 5x(9x + 5) + -17 [1 * 8 + 5x * 8] + 5x = 5x(9x + 5) + -17 [8 + 40x] + 5x = 5x(9x + 5) + -17 Combine like terms: 40x + 5x = 45x 8 + 45x = 5x(9x + 5) + -17 Reorder the terms: 8 + 45x = 5x(5 + 9x) + -17 8 + 45x = (5 * 5x + 9x * 5x) + -17 8 + 45x = (25x + 45x2) + -17 Reorder the terms: 8 + 45x = -17 + 25x + 45x2 Solving 8 + 45x = -17 + 25x + 45x2 Solving for variable 'x'. Reorder the terms: 8 + 17 + 45x + -25x + -45x2 = -17 + 25x + 45x2 + 17 + -25x + -45x2 Combine like terms: 8 + 17 = 25 25 + 45x + -25x + -45x2 = -17 + 25x + 45x2 + 17 + -25x + -45x2 Combine like terms: 45x + -25x = 20x 25 + 20x + -45x2 = -17 + 25x + 45x2 + 17 + -25x + -45x2 Reorder the terms: 25 + 20x + -45x2 = -17 + 17 + 25x + -25x + 45x2 + -45x2 Combine like terms: -17 + 17 = 0 25 + 20x + -45x2 = 0 + 25x + -25x + 45x2 + -45x2 25 + 20x + -45x2 = 25x + -25x + 45x2 + -45x2 Combine like terms: 25x + -25x = 0 25 + 20x + -45x2 = 0 + 45x2 + -45x2 25 + 20x + -45x2 = 45x2 + -45x2 Combine like terms: 45x2 + -45x2 = 0 25 + 20x + -45x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(5 + 4x + -9x2) = 0 Factor a trinomial. 5((1 + -1x)(5 + 9x)) = 0 Ignore the factor 5.Subproblem 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 '(5 + 9x)' equal to zero and attempt to solve: Simplifying 5 + 9x = 0 Solving 5 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 9x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9x = 0 + -5 9x = 0 + -5 Combine like terms: 0 + -5 = -5 9x = -5 Divide each side by '9'. x = -0.5555555556 Simplifying x = -0.5555555556Solution
x = {1, -0.5555555556}
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