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