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Simplifying -6x2 = 3x + 2 Reorder the terms: -6x2 = 2 + 3x Solving -6x2 = 2 + 3x Solving for variable 'x'. Reorder the terms: -2 + -3x + -6x2 = 2 + 3x + -2 + -3x Reorder the terms: -2 + -3x + -6x2 = 2 + -2 + 3x + -3x Combine like terms: 2 + -2 = 0 -2 + -3x + -6x2 = 0 + 3x + -3x -2 + -3x + -6x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -2 + -3x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 3x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 3x + 6x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + 6x2 = 0 Solving 2 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3333333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.5x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.5x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + -0.3333333333 0.5x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.5x + x2 = -0.3333333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.3333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.3333333333 + 0.0625 Combine like terms: -0.3333333333 + 0.0625 = -0.2708333333 0.0625 + 0.5x + x2 = -0.2708333333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.2708333333 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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