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Simplifying 3(3x + -1) + 5(5x + 1) = 3(5x + 1)(3x + -1) Reorder the terms: 3(-1 + 3x) + 5(5x + 1) = 3(5x + 1)(3x + -1) (-1 * 3 + 3x * 3) + 5(5x + 1) = 3(5x + 1)(3x + -1) (-3 + 9x) + 5(5x + 1) = 3(5x + 1)(3x + -1) Reorder the terms: -3 + 9x + 5(1 + 5x) = 3(5x + 1)(3x + -1) -3 + 9x + (1 * 5 + 5x * 5) = 3(5x + 1)(3x + -1) -3 + 9x + (5 + 25x) = 3(5x + 1)(3x + -1) Reorder the terms: -3 + 5 + 9x + 25x = 3(5x + 1)(3x + -1) Combine like terms: -3 + 5 = 2 2 + 9x + 25x = 3(5x + 1)(3x + -1) Combine like terms: 9x + 25x = 34x 2 + 34x = 3(5x + 1)(3x + -1) Reorder the terms: 2 + 34x = 3(1 + 5x)(3x + -1) Reorder the terms: 2 + 34x = 3(1 + 5x)(-1 + 3x) Multiply (1 + 5x) * (-1 + 3x) 2 + 34x = 3(1(-1 + 3x) + 5x * (-1 + 3x)) 2 + 34x = 3((-1 * 1 + 3x * 1) + 5x * (-1 + 3x)) 2 + 34x = 3((-1 + 3x) + 5x * (-1 + 3x)) 2 + 34x = 3(-1 + 3x + (-1 * 5x + 3x * 5x)) 2 + 34x = 3(-1 + 3x + (-5x + 15x2)) Combine like terms: 3x + -5x = -2x 2 + 34x = 3(-1 + -2x + 15x2) 2 + 34x = (-1 * 3 + -2x * 3 + 15x2 * 3) 2 + 34x = (-3 + -6x + 45x2) Solving 2 + 34x = -3 + -6x + 45x2 Solving for variable 'x'. Reorder the terms: 2 + 3 + 34x + 6x + -45x2 = -3 + -6x + 45x2 + 3 + 6x + -45x2 Combine like terms: 2 + 3 = 5 5 + 34x + 6x + -45x2 = -3 + -6x + 45x2 + 3 + 6x + -45x2 Combine like terms: 34x + 6x = 40x 5 + 40x + -45x2 = -3 + -6x + 45x2 + 3 + 6x + -45x2 Reorder the terms: 5 + 40x + -45x2 = -3 + 3 + -6x + 6x + 45x2 + -45x2 Combine like terms: -3 + 3 = 0 5 + 40x + -45x2 = 0 + -6x + 6x + 45x2 + -45x2 5 + 40x + -45x2 = -6x + 6x + 45x2 + -45x2 Combine like terms: -6x + 6x = 0 5 + 40x + -45x2 = 0 + 45x2 + -45x2 5 + 40x + -45x2 = 45x2 + -45x2 Combine like terms: 45x2 + -45x2 = 0 5 + 40x + -45x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 8x + -9x2) = 0 Factor a trinomial. 5((1 + -1x)(1 + 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 '(1 + 9x)' equal to zero and attempt to solve: Simplifying 1 + 9x = 0 Solving 1 + 9x = 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 + 9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x = 0 + -1 9x = 0 + -1 Combine like terms: 0 + -1 = -1 9x = -1 Divide each side by '9'. x = -0.1111111111 Simplifying x = -0.1111111111Solution
x = {1, -0.1111111111}
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