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Simplifying 3x(2x2 + -1x + 3) = 6x2 + -3x Reorder the terms: 3x(3 + -1x + 2x2) = 6x2 + -3x (3 * 3x + -1x * 3x + 2x2 * 3x) = 6x2 + -3x (9x + -3x2 + 6x3) = 6x2 + -3x Reorder the terms: 9x + -3x2 + 6x3 = -3x + 6x2 Solving 9x + -3x2 + 6x3 = -3x + 6x2 Solving for variable 'x'. Reorder the terms: 9x + 3x + -3x2 + -6x2 + 6x3 = -3x + 6x2 + 3x + -6x2 Combine like terms: 9x + 3x = 12x 12x + -3x2 + -6x2 + 6x3 = -3x + 6x2 + 3x + -6x2 Combine like terms: -3x2 + -6x2 = -9x2 12x + -9x2 + 6x3 = -3x + 6x2 + 3x + -6x2 Reorder the terms: 12x + -9x2 + 6x3 = -3x + 3x + 6x2 + -6x2 Combine like terms: -3x + 3x = 0 12x + -9x2 + 6x3 = 0 + 6x2 + -6x2 12x + -9x2 + 6x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 12x + -9x2 + 6x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(4 + -3x + 2x2) = 0 Ignore the factor 3.Subproblem 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 '(4 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + 2x2 = 0 Solving 4 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -1.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.5x + x2 = 0 + -2 -1.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.5x + x2 = -2 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -2 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + -1.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -1.4375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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