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Simplifying 6x2 + -8x = -6 Reorder the terms: -8x + 6x2 = -6 Solving -8x + 6x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + -8x + 6x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -8x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -4x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 3x2 = 0 Solving 3 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1.333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.333333333x + x2 = 0 + -1 -1.333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.333333333x + x2 = -1 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -1 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -1 + 0.4444444442 Combine like terms: -1 + 0.4444444442 = -0.5555555558 0.4444444442 + -1.333333333x + x2 = -0.5555555558 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -0.5555555558 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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