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Simplifying 0 = 6x2 + -5x + 1 Reorder the terms: 0 = 1 + -5x + 6x2 Solving 0 = 1 + -5x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 5x + -6x2 = 1 + -5x + 6x2 + -1 + 5x + -6x2 Reorder the terms: -1 + 5x + -6x2 = 1 + -1 + -5x + 5x + 6x2 + -6x2 Combine like terms: 1 + -1 = 0 -1 + 5x + -6x2 = 0 + -5x + 5x + 6x2 + -6x2 -1 + 5x + -6x2 = -5x + 5x + 6x2 + -6x2 Combine like terms: -5x + 5x = 0 -1 + 5x + -6x2 = 0 + 6x2 + -6x2 -1 + 5x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -1 + 5x + -6x2 = 0 Factor a trinomial. (-1 + 2x)(1 + -3x) = 0Subproblem 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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