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Simplifying (5x + -1)(5x + -1) + -1(3x + 2)(5x + -1) = 0 Reorder the terms: (-1 + 5x)(5x + -1) + -1(3x + 2)(5x + -1) = 0 Reorder the terms: (-1 + 5x)(-1 + 5x) + -1(3x + 2)(5x + -1) = 0 Multiply (-1 + 5x) * (-1 + 5x) (-1(-1 + 5x) + 5x * (-1 + 5x)) + -1(3x + 2)(5x + -1) = 0 ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) + -1(3x + 2)(5x + -1) = 0 ((1 + -5x) + 5x * (-1 + 5x)) + -1(3x + 2)(5x + -1) = 0 (1 + -5x + (-1 * 5x + 5x * 5x)) + -1(3x + 2)(5x + -1) = 0 (1 + -5x + (-5x + 25x2)) + -1(3x + 2)(5x + -1) = 0 Combine like terms: -5x + -5x = -10x (1 + -10x + 25x2) + -1(3x + 2)(5x + -1) = 0 Reorder the terms: 1 + -10x + 25x2 + -1(2 + 3x)(5x + -1) = 0 Reorder the terms: 1 + -10x + 25x2 + -1(2 + 3x)(-1 + 5x) = 0 Multiply (2 + 3x) * (-1 + 5x) 1 + -10x + 25x2 + -1(2(-1 + 5x) + 3x * (-1 + 5x)) = 0 1 + -10x + 25x2 + -1((-1 * 2 + 5x * 2) + 3x * (-1 + 5x)) = 0 1 + -10x + 25x2 + -1((-2 + 10x) + 3x * (-1 + 5x)) = 0 1 + -10x + 25x2 + -1(-2 + 10x + (-1 * 3x + 5x * 3x)) = 0 1 + -10x + 25x2 + -1(-2 + 10x + (-3x + 15x2)) = 0 Combine like terms: 10x + -3x = 7x 1 + -10x + 25x2 + -1(-2 + 7x + 15x2) = 0 1 + -10x + 25x2 + (-2 * -1 + 7x * -1 + 15x2 * -1) = 0 1 + -10x + 25x2 + (2 + -7x + -15x2) = 0 Reorder the terms: 1 + 2 + -10x + -7x + 25x2 + -15x2 = 0 Combine like terms: 1 + 2 = 3 3 + -10x + -7x + 25x2 + -15x2 = 0 Combine like terms: -10x + -7x = -17x 3 + -17x + 25x2 + -15x2 = 0 Combine like terms: 25x2 + -15x2 = 10x2 3 + -17x + 10x2 = 0 Solving 3 + -17x + 10x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -5x)(3 + -2x) = 0Subproblem 1
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 = 0.2Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0.2, 1.5}
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