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Simplifying 0 = -2x2 + 3x + -1 Reorder the terms: 0 = -1 + 3x + -2x2 Solving 0 = -1 + 3x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 1 = 1 1 + -3x + 2x2 = -1 + 3x + -2x2 + 1 + -3x + 2x2 Reorder the terms: 1 + -3x + 2x2 = -1 + 1 + 3x + -3x + -2x2 + 2x2 Combine like terms: -1 + 1 = 0 1 + -3x + 2x2 = 0 + 3x + -3x + -2x2 + 2x2 1 + -3x + 2x2 = 3x + -3x + -2x2 + 2x2 Combine like terms: 3x + -3x = 0 1 + -3x + 2x2 = 0 + -2x2 + 2x2 1 + -3x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 1 + -3x + 2x2 = 0 Factor a trinomial. (1 + -2x)(1 + -1x) = 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 + -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 = 1Solution
x = {0.5, 1}
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