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Simplifying 1 = 2x2 + -3x + 1 Reorder the terms: 1 = 1 + -3x + 2x2 Add '-1' to each side of the equation. 1 + -1 = 1 + -3x + -1 + 2x2 Combine like terms: 1 + -1 = 0 0 = 1 + -3x + -1 + 2x2 Reorder the terms: 0 = 1 + -1 + -3x + 2x2 Combine like terms: 1 + -1 = 0 0 = 0 + -3x + 2x2 0 = -3x + 2x2 Solving 0 = -3x + 2x2 Solving for variable 'x'. Remove the zero: 3x + -2x2 = -3x + 2x2 + 3x + -2x2 Reorder the terms: 3x + -2x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 3x + -2x2 = 0 + 2x2 + -2x2 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(3 + -2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
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