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Simplifying x + -1(5 + -1x) = 4x + -1(2x + -1)(2x + 1) x + (5 * -1 + -1x * -1) = 4x + -1(2x + -1)(2x + 1) x + (-5 + 1x) = 4x + -1(2x + -1)(2x + 1) Reorder the terms: -5 + x + 1x = 4x + -1(2x + -1)(2x + 1) Combine like terms: x + 1x = 2x -5 + 2x = 4x + -1(2x + -1)(2x + 1) Reorder the terms: -5 + 2x = 4x + -1(-1 + 2x)(2x + 1) Reorder the terms: -5 + 2x = 4x + -1(-1 + 2x)(1 + 2x) Multiply (-1 + 2x) * (1 + 2x) -5 + 2x = 4x + -1(-1(1 + 2x) + 2x * (1 + 2x)) -5 + 2x = 4x + -1((1 * -1 + 2x * -1) + 2x * (1 + 2x)) -5 + 2x = 4x + -1((-1 + -2x) + 2x * (1 + 2x)) -5 + 2x = 4x + -1(-1 + -2x + (1 * 2x + 2x * 2x)) -5 + 2x = 4x + -1(-1 + -2x + (2x + 4x2)) Combine like terms: -2x + 2x = 0 -5 + 2x = 4x + -1(-1 + 0 + 4x2) -5 + 2x = 4x + -1(-1 + 4x2) -5 + 2x = 4x + (-1 * -1 + 4x2 * -1) -5 + 2x = 4x + (1 + -4x2) Reorder the terms: -5 + 2x = 1 + 4x + -4x2 Solving -5 + 2x = 1 + 4x + -4x2 Solving for variable 'x'. Reorder the terms: -5 + -1 + 2x + -4x + 4x2 = 1 + 4x + -4x2 + -1 + -4x + 4x2 Combine like terms: -5 + -1 = -6 -6 + 2x + -4x + 4x2 = 1 + 4x + -4x2 + -1 + -4x + 4x2 Combine like terms: 2x + -4x = -2x -6 + -2x + 4x2 = 1 + 4x + -4x2 + -1 + -4x + 4x2 Reorder the terms: -6 + -2x + 4x2 = 1 + -1 + 4x + -4x + -4x2 + 4x2 Combine like terms: 1 + -1 = 0 -6 + -2x + 4x2 = 0 + 4x + -4x + -4x2 + 4x2 -6 + -2x + 4x2 = 4x + -4x + -4x2 + 4x2 Combine like terms: 4x + -4x = 0 -6 + -2x + 4x2 = 0 + -4x2 + 4x2 -6 + -2x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -6 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -1x + 2x2) = 0 Factor a trinomial. 2((-1 + -1x)(3 + -2x)) = 0 Ignore the factor 2.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 '(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 = {-1, 1.5}
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