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Simplifying 3(5x + 1) + (5x + 1)(5x + 1) = (5x + 1)(3x + -3) Reorder the terms: 3(1 + 5x) + (5x + 1)(5x + 1) = (5x + 1)(3x + -3) (1 * 3 + 5x * 3) + (5x + 1)(5x + 1) = (5x + 1)(3x + -3) (3 + 15x) + (5x + 1)(5x + 1) = (5x + 1)(3x + -3) Reorder the terms: 3 + 15x + (1 + 5x)(5x + 1) = (5x + 1)(3x + -3) Reorder the terms: 3 + 15x + (1 + 5x)(1 + 5x) = (5x + 1)(3x + -3) Multiply (1 + 5x) * (1 + 5x) 3 + 15x + (1(1 + 5x) + 5x * (1 + 5x)) = (5x + 1)(3x + -3) 3 + 15x + ((1 * 1 + 5x * 1) + 5x * (1 + 5x)) = (5x + 1)(3x + -3) 3 + 15x + ((1 + 5x) + 5x * (1 + 5x)) = (5x + 1)(3x + -3) 3 + 15x + (1 + 5x + (1 * 5x + 5x * 5x)) = (5x + 1)(3x + -3) 3 + 15x + (1 + 5x + (5x + 25x2)) = (5x + 1)(3x + -3) Combine like terms: 5x + 5x = 10x 3 + 15x + (1 + 10x + 25x2) = (5x + 1)(3x + -3) Reorder the terms: 3 + 1 + 15x + 10x + 25x2 = (5x + 1)(3x + -3) Combine like terms: 3 + 1 = 4 4 + 15x + 10x + 25x2 = (5x + 1)(3x + -3) Combine like terms: 15x + 10x = 25x 4 + 25x + 25x2 = (5x + 1)(3x + -3) Reorder the terms: 4 + 25x + 25x2 = (1 + 5x)(3x + -3) Reorder the terms: 4 + 25x + 25x2 = (1 + 5x)(-3 + 3x) Multiply (1 + 5x) * (-3 + 3x) 4 + 25x + 25x2 = (1(-3 + 3x) + 5x * (-3 + 3x)) 4 + 25x + 25x2 = ((-3 * 1 + 3x * 1) + 5x * (-3 + 3x)) 4 + 25x + 25x2 = ((-3 + 3x) + 5x * (-3 + 3x)) 4 + 25x + 25x2 = (-3 + 3x + (-3 * 5x + 3x * 5x)) 4 + 25x + 25x2 = (-3 + 3x + (-15x + 15x2)) Combine like terms: 3x + -15x = -12x 4 + 25x + 25x2 = (-3 + -12x + 15x2) Solving 4 + 25x + 25x2 = -3 + -12x + 15x2 Solving for variable 'x'. Reorder the terms: 4 + 3 + 25x + 12x + 25x2 + -15x2 = -3 + -12x + 15x2 + 3 + 12x + -15x2 Combine like terms: 4 + 3 = 7 7 + 25x + 12x + 25x2 + -15x2 = -3 + -12x + 15x2 + 3 + 12x + -15x2 Combine like terms: 25x + 12x = 37x 7 + 37x + 25x2 + -15x2 = -3 + -12x + 15x2 + 3 + 12x + -15x2 Combine like terms: 25x2 + -15x2 = 10x2 7 + 37x + 10x2 = -3 + -12x + 15x2 + 3 + 12x + -15x2 Reorder the terms: 7 + 37x + 10x2 = -3 + 3 + -12x + 12x + 15x2 + -15x2 Combine like terms: -3 + 3 = 0 7 + 37x + 10x2 = 0 + -12x + 12x + 15x2 + -15x2 7 + 37x + 10x2 = -12x + 12x + 15x2 + -15x2 Combine like terms: -12x + 12x = 0 7 + 37x + 10x2 = 0 + 15x2 + -15x2 7 + 37x + 10x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 7 + 37x + 10x2 = 0 Factor a trinomial. (7 + 2x)(1 + 5x) = 0Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Solution
x = {-3.5, -0.2}
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