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Simplifying 12x2 + 4x + 6 = 0 Reorder the terms: 6 + 4x + 12x2 = 0 Solving 6 + 4x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 2x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x + 6x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + 6x2 = 0 Solving 3 + 2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.3333333333x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.3333333333x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.3333333333x + x2 = 0 + -0.5 0.3333333333x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.3333333333x + x2 = -0.5 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.5 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.5 + 0.02777777779 Combine like terms: -0.5 + 0.02777777779 = -0.47222222221 0.02777777779 + 0.3333333333x + x2 = -0.47222222221 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.47222222221 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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