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Simplifying 27x2 + -30x + 12 = 0 Reorder the terms: 12 + -30x + 27x2 = 0 Solving 12 + -30x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -10x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -10x + 9x2)' equal to zero and attempt to solve: Simplifying 4 + -10x + 9x2 = 0 Solving 4 + -10x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -1.111111111x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -1.111111111x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -1.111111111x + x2 = 0 + -0.4444444444 -1.111111111x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -1.111111111x + x2 = -0.4444444444 The x term is -1.111111111x. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111x + 0.3086419752 + x2 = -0.4444444444 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = -0.4444444444 + 0.3086419752 Combine like terms: -0.4444444444 + 0.3086419752 = -0.1358024692 0.3086419752 + -1.111111111x + x2 = -0.1358024692 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = -0.1358024692 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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