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Simplifying 6(5x + -1)(5x + -1) + 4 = -14(5x + -1) Reorder the terms: 6(-1 + 5x)(5x + -1) + 4 = -14(5x + -1) Reorder the terms: 6(-1 + 5x)(-1 + 5x) + 4 = -14(5x + -1) Multiply (-1 + 5x) * (-1 + 5x) 6(-1(-1 + 5x) + 5x * (-1 + 5x)) + 4 = -14(5x + -1) 6((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) + 4 = -14(5x + -1) 6((1 + -5x) + 5x * (-1 + 5x)) + 4 = -14(5x + -1) 6(1 + -5x + (-1 * 5x + 5x * 5x)) + 4 = -14(5x + -1) 6(1 + -5x + (-5x + 25x2)) + 4 = -14(5x + -1) Combine like terms: -5x + -5x = -10x 6(1 + -10x + 25x2) + 4 = -14(5x + -1) (1 * 6 + -10x * 6 + 25x2 * 6) + 4 = -14(5x + -1) (6 + -60x + 150x2) + 4 = -14(5x + -1) Reorder the terms: 6 + 4 + -60x + 150x2 = -14(5x + -1) Combine like terms: 6 + 4 = 10 10 + -60x + 150x2 = -14(5x + -1) Reorder the terms: 10 + -60x + 150x2 = -14(-1 + 5x) 10 + -60x + 150x2 = (-1 * -14 + 5x * -14) 10 + -60x + 150x2 = (14 + -70x) Solving 10 + -60x + 150x2 = 14 + -70x Solving for variable 'x'. Reorder the terms: 10 + -14 + -60x + 70x + 150x2 = 14 + -70x + -14 + 70x Combine like terms: 10 + -14 = -4 -4 + -60x + 70x + 150x2 = 14 + -70x + -14 + 70x Combine like terms: -60x + 70x = 10x -4 + 10x + 150x2 = 14 + -70x + -14 + 70x Reorder the terms: -4 + 10x + 150x2 = 14 + -14 + -70x + 70x Combine like terms: 14 + -14 = 0 -4 + 10x + 150x2 = 0 + -70x + 70x -4 + 10x + 150x2 = -70x + 70x Combine like terms: -70x + 70x = 0 -4 + 10x + 150x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 5x + 75x2) = 0 Factor a trinomial. 2((-1 + -5x)(2 + -15x)) = 0 Ignore the factor 2.Subproblem 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 '(2 + -15x)' equal to zero and attempt to solve: Simplifying 2 + -15x = 0 Solving 2 + -15x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -15x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -15x = 0 + -2 -15x = 0 + -2 Combine like terms: 0 + -2 = -2 -15x = -2 Divide each side by '-15'. x = 0.1333333333 Simplifying x = 0.1333333333Solution
x = {-0.2, 0.1333333333}
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