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Simplifying 81a2 + 30a + 6 = 0 Reorder the terms: 6 + 30a + 81a2 = 0 Solving 6 + 30a + 81a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 10a + 27a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + 10a + 27a2)' equal to zero and attempt to solve: Simplifying 2 + 10a + 27a2 = 0 Solving 2 + 10a + 27a2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.07407407407 + 0.3703703704a + a2 = 0 Move the constant term to the right: Add '-0.07407407407' to each side of the equation. 0.07407407407 + 0.3703703704a + -0.07407407407 + a2 = 0 + -0.07407407407 Reorder the terms: 0.07407407407 + -0.07407407407 + 0.3703703704a + a2 = 0 + -0.07407407407 Combine like terms: 0.07407407407 + -0.07407407407 = 0.00000000000 0.00000000000 + 0.3703703704a + a2 = 0 + -0.07407407407 0.3703703704a + a2 = 0 + -0.07407407407 Combine like terms: 0 + -0.07407407407 = -0.07407407407 0.3703703704a + a2 = -0.07407407407 The a term is 0.3703703704a. Take half its coefficient (0.1851851852). Square it (0.03429355282) and add it to both sides. Add '0.03429355282' to each side of the equation. 0.3703703704a + 0.03429355282 + a2 = -0.07407407407 + 0.03429355282 Reorder the terms: 0.03429355282 + 0.3703703704a + a2 = -0.07407407407 + 0.03429355282 Combine like terms: -0.07407407407 + 0.03429355282 = -0.03978052125 0.03429355282 + 0.3703703704a + a2 = -0.03978052125 Factor a perfect square on the left side: (a + 0.1851851852)(a + 0.1851851852) = -0.03978052125 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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