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Simplifying 18a2 + 20a + 4 = 0 Reorder the terms: 4 + 20a + 18a2 = 0 Solving 4 + 20a + 18a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 10a + 9a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 10a + 9a2)' equal to zero and attempt to solve: Simplifying 2 + 10a + 9a2 = 0 Solving 2 + 10a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 1.111111111a + a2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 1.111111111a + -0.2222222222 + a2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 1.111111111a + a2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 1.111111111a + a2 = 0 + -0.2222222222 1.111111111a + a2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 1.111111111a + a2 = -0.2222222222 The a term is 1.111111111a. 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. 1.111111111a + 0.3086419752 + a2 = -0.2222222222 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111a + a2 = -0.2222222222 + 0.3086419752 Combine like terms: -0.2222222222 + 0.3086419752 = 0.086419753 0.3086419752 + 1.111111111a + a2 = 0.086419753 Factor a perfect square on the left side: (a + 0.5555555555)(a + 0.5555555555) = 0.086419753 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting (a + 0.5555555555) equal to 0.293972368 and -0.293972368.Subproblem 1
a + 0.5555555555 = 0.293972368 Simplifying a + 0.5555555555 = 0.293972368 Reorder the terms: 0.5555555555 + a = 0.293972368 Solving 0.5555555555 + a = 0.293972368 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + a = 0.293972368 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + a = 0.293972368 + -0.5555555555 a = 0.293972368 + -0.5555555555 Combine like terms: 0.293972368 + -0.5555555555 = -0.2615831875 a = -0.2615831875 Simplifying a = -0.2615831875Subproblem 2
a + 0.5555555555 = -0.293972368 Simplifying a + 0.5555555555 = -0.293972368 Reorder the terms: 0.5555555555 + a = -0.293972368 Solving 0.5555555555 + a = -0.293972368 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + a = -0.293972368 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + a = -0.293972368 + -0.5555555555 a = -0.293972368 + -0.5555555555 Combine like terms: -0.293972368 + -0.5555555555 = -0.8495279235 a = -0.8495279235 Simplifying a = -0.8495279235Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.2615831875, -0.8495279235}Solution
a = {-0.2615831875, -0.8495279235}
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