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