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Simplifying -6x2 = 5x + 1 Reorder the terms: -6x2 = 1 + 5x Solving -6x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: -1 + -5x + -6x2 = 1 + 5x + -1 + -5x Reorder the terms: -1 + -5x + -6x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 -1 + -5x + -6x2 = 0 + 5x + -5x -1 + -5x + -6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -1 + -5x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 5x + 6x2) = 0 Factor a trinomial. -1((1 + 2x)(1 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-0.5, -0.3333333333}
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