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Simplifying 0 = 6a2 + 2a + 1 Reorder the terms: 0 = 1 + 2a + 6a2 Solving 0 = 1 + 2a + 6a2 Solving for variable 'a'. Combine like terms: 0 + -1 = -1 -1 + -2a + -6a2 = 1 + 2a + 6a2 + -1 + -2a + -6a2 Reorder the terms: -1 + -2a + -6a2 = 1 + -1 + 2a + -2a + 6a2 + -6a2 Combine like terms: 1 + -1 = 0 -1 + -2a + -6a2 = 0 + 2a + -2a + 6a2 + -6a2 -1 + -2a + -6a2 = 2a + -2a + 6a2 + -6a2 Combine like terms: 2a + -2a = 0 -1 + -2a + -6a2 = 0 + 6a2 + -6a2 -1 + -2a + -6a2 = 6a2 + -6a2 Combine like terms: 6a2 + -6a2 = 0 -1 + -2a + -6a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 2a + 6a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 2a + 6a2)' equal to zero and attempt to solve: Simplifying 1 + 2a + 6a2 = 0 Solving 1 + 2a + 6a2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 0.3333333333a + a2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.3333333333a + -0.1666666667 + a2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.3333333333a + a2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.3333333333a + a2 = 0 + -0.1666666667 0.3333333333a + a2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.3333333333a + a2 = -0.1666666667 The a term is 0.3333333333a. 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. 0.3333333333a + 0.02777777779 + a2 = -0.1666666667 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333a + a2 = -0.1666666667 + 0.02777777779 Combine like terms: -0.1666666667 + 0.02777777779 = -0.13888888891 0.02777777779 + 0.3333333333a + a2 = -0.13888888891 Factor a perfect square on the left side: (a + 0.1666666667)(a + 0.1666666667) = -0.13888888891 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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