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Simplifying 3(5x + 1) + (5x + 1)(5x + 1) = (5x + 1) Reorder the terms: 3(1 + 5x) + (5x + 1)(5x + 1) = (5x + 1) (1 * 3 + 5x * 3) + (5x + 1)(5x + 1) = (5x + 1) (3 + 15x) + (5x + 1)(5x + 1) = (5x + 1) Reorder the terms: 3 + 15x + (1 + 5x)(5x + 1) = (5x + 1) Reorder the terms: 3 + 15x + (1 + 5x)(1 + 5x) = (5x + 1) Multiply (1 + 5x) * (1 + 5x) 3 + 15x + (1(1 + 5x) + 5x * (1 + 5x)) = (5x + 1) 3 + 15x + ((1 * 1 + 5x * 1) + 5x * (1 + 5x)) = (5x + 1) 3 + 15x + ((1 + 5x) + 5x * (1 + 5x)) = (5x + 1) 3 + 15x + (1 + 5x + (1 * 5x + 5x * 5x)) = (5x + 1) 3 + 15x + (1 + 5x + (5x + 25x2)) = (5x + 1) Combine like terms: 5x + 5x = 10x 3 + 15x + (1 + 10x + 25x2) = (5x + 1) Reorder the terms: 3 + 1 + 15x + 10x + 25x2 = (5x + 1) Combine like terms: 3 + 1 = 4 4 + 15x + 10x + 25x2 = (5x + 1) Combine like terms: 15x + 10x = 25x 4 + 25x + 25x2 = (5x + 1) Reorder the terms: 4 + 25x + 25x2 = (1 + 5x) Remove parenthesis around (1 + 5x) 4 + 25x + 25x2 = 1 + 5x Solving 4 + 25x + 25x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: 4 + -1 + 25x + -5x + 25x2 = 1 + 5x + -1 + -5x Combine like terms: 4 + -1 = 3 3 + 25x + -5x + 25x2 = 1 + 5x + -1 + -5x Combine like terms: 25x + -5x = 20x 3 + 20x + 25x2 = 1 + 5x + -1 + -5x Reorder the terms: 3 + 20x + 25x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 3 + 20x + 25x2 = 0 + 5x + -5x 3 + 20x + 25x2 = 5x + -5x Combine like terms: 5x + -5x = 0 3 + 20x + 25x2 = 0 Factor a trinomial. (3 + 5x)(1 + 5x) = 0Subproblem 1
Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Subproblem 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 = {-0.6, -0.2}
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