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Simplifying 12a(12a) + 3a + -8a + -2 = 0 Remove parenthesis around (12a) 12a * 12a + 3a + -8a + -2 = 0 Reorder the terms for easier multiplication: 12 * 12a * a + 3a + -8a + -2 = 0 Multiply 12 * 12 144a * a + 3a + -8a + -2 = 0 Multiply a * a 144a2 + 3a + -8a + -2 = 0 Reorder the terms: -2 + 3a + -8a + 144a2 = 0 Combine like terms: 3a + -8a = -5a -2 + -5a + 144a2 = 0 Solving -2 + -5a + 144a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. -0.01388888889 + -0.03472222222a + a2 = 0 Move the constant term to the right: Add '0.01388888889' to each side of the equation. -0.01388888889 + -0.03472222222a + 0.01388888889 + a2 = 0 + 0.01388888889 Reorder the terms: -0.01388888889 + 0.01388888889 + -0.03472222222a + a2 = 0 + 0.01388888889 Combine like terms: -0.01388888889 + 0.01388888889 = 0.00000000000 0.00000000000 + -0.03472222222a + a2 = 0 + 0.01388888889 -0.03472222222a + a2 = 0 + 0.01388888889 Combine like terms: 0 + 0.01388888889 = 0.01388888889 -0.03472222222a + a2 = 0.01388888889 The a term is -0.03472222222a. Take half its coefficient (-0.01736111111). Square it (0.0003014081790) and add it to both sides. Add '0.0003014081790' to each side of the equation. -0.03472222222a + 0.0003014081790 + a2 = 0.01388888889 + 0.0003014081790 Reorder the terms: 0.0003014081790 + -0.03472222222a + a2 = 0.01388888889 + 0.0003014081790 Combine like terms: 0.01388888889 + 0.0003014081790 = 0.014190297069 0.0003014081790 + -0.03472222222a + a2 = 0.014190297069 Factor a perfect square on the left side: (a + -0.01736111111)(a + -0.01736111111) = 0.014190297069 Calculate the square root of the right side: 0.119123033 Break this problem into two subproblems by setting (a + -0.01736111111) equal to 0.119123033 and -0.119123033.Subproblem 1
a + -0.01736111111 = 0.119123033 Simplifying a + -0.01736111111 = 0.119123033 Reorder the terms: -0.01736111111 + a = 0.119123033 Solving -0.01736111111 + a = 0.119123033 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.01736111111' to each side of the equation. -0.01736111111 + 0.01736111111 + a = 0.119123033 + 0.01736111111 Combine like terms: -0.01736111111 + 0.01736111111 = 0.00000000000 0.00000000000 + a = 0.119123033 + 0.01736111111 a = 0.119123033 + 0.01736111111 Combine like terms: 0.119123033 + 0.01736111111 = 0.13648414411 a = 0.13648414411 Simplifying a = 0.13648414411Subproblem 2
a + -0.01736111111 = -0.119123033 Simplifying a + -0.01736111111 = -0.119123033 Reorder the terms: -0.01736111111 + a = -0.119123033 Solving -0.01736111111 + a = -0.119123033 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.01736111111' to each side of the equation. -0.01736111111 + 0.01736111111 + a = -0.119123033 + 0.01736111111 Combine like terms: -0.01736111111 + 0.01736111111 = 0.00000000000 0.00000000000 + a = -0.119123033 + 0.01736111111 a = -0.119123033 + 0.01736111111 Combine like terms: -0.119123033 + 0.01736111111 = -0.10176192189 a = -0.10176192189 Simplifying a = -0.10176192189Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.13648414411, -0.10176192189}
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