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Simplifying 36a2 + 10a + 8 = 0 Reorder the terms: 8 + 10a + 36a2 = 0 Solving 8 + 10a + 36a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 5a + 18a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 5a + 18a2)' equal to zero and attempt to solve: Simplifying 4 + 5a + 18a2 = 0 Solving 4 + 5a + 18a2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2222222222 + 0.2777777778a + a2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 0.2777777778a + -0.2222222222 + a2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 0.2777777778a + a2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 0.2777777778a + a2 = 0 + -0.2222222222 0.2777777778a + a2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 0.2777777778a + a2 = -0.2222222222 The a term is 0.2777777778a. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778a + 0.01929012346 + a2 = -0.2222222222 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778a + a2 = -0.2222222222 + 0.01929012346 Combine like terms: -0.2222222222 + 0.01929012346 = -0.20293209874 0.01929012346 + 0.2777777778a + a2 = -0.20293209874 Factor a perfect square on the left side: (a + 0.1388888889)(a + 0.1388888889) = -0.20293209874 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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