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Simplifying x = 3x2 + 2x + 6 Reorder the terms: x = 6 + 2x + 3x2 Solving x = 6 + 2x + 3x2 Solving for variable 'x'. Reorder the terms: -6 + x + -2x + -3x2 = 6 + 2x + 3x2 + -6 + -2x + -3x2 Combine like terms: x + -2x = -1x -6 + -1x + -3x2 = 6 + 2x + 3x2 + -6 + -2x + -3x2 Reorder the terms: -6 + -1x + -3x2 = 6 + -6 + 2x + -2x + 3x2 + -3x2 Combine like terms: 6 + -6 = 0 -6 + -1x + -3x2 = 0 + 2x + -2x + 3x2 + -3x2 -6 + -1x + -3x2 = 2x + -2x + 3x2 + -3x2 Combine like terms: 2x + -2x = 0 -6 + -1x + -3x2 = 0 + 3x2 + -3x2 -6 + -1x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + -1x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + x + 3x2 = 0 Solving 6 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.3333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 0.3333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.3333333333x + x2 = 0 + -2 0.3333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.3333333333x + x2 = -2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = -2 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + 0.3333333333x + x2 = -1.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.75 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. The solution to this equation could not be determined.
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