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Simplifying 2x = 6x2 + 4 Reorder the terms: 2x = 4 + 6x2 Solving 2x = 4 + 6x2 Solving for variable 'x'. Reorder the terms: -4 + 2x + -6x2 = 4 + 6x2 + -4 + -6x2 Reorder the terms: -4 + 2x + -6x2 = 4 + -4 + 6x2 + -6x2 Combine like terms: 4 + -4 = 0 -4 + 2x + -6x2 = 0 + 6x2 + -6x2 -4 + 2x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + 2x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x + -3x2)' equal to zero and attempt to solve: Simplifying -2 + x + -3x2 = 0 Solving -2 + x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.6666666667 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.3333333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.3333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + -0.6666666667 -0.3333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.3333333333x + x2 = -0.6666666667 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 = -0.6666666667 + 0.25 Reorder the terms: 0.25 + -0.3333333333x + x2 = -0.6666666667 + 0.25 Combine like terms: -0.6666666667 + 0.25 = -0.4166666667 0.25 + -0.3333333333x + x2 = -0.4166666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.4166666667 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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