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Simplifying 39a2 + 33a + 4 = 0 Reorder the terms: 4 + 33a + 39a2 = 0 Solving 4 + 33a + 39a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. 0.1025641026 + 0.8461538462a + a2 = 0 Move the constant term to the right: Add '-0.1025641026' to each side of the equation. 0.1025641026 + 0.8461538462a + -0.1025641026 + a2 = 0 + -0.1025641026 Reorder the terms: 0.1025641026 + -0.1025641026 + 0.8461538462a + a2 = 0 + -0.1025641026 Combine like terms: 0.1025641026 + -0.1025641026 = 0.0000000000 0.0000000000 + 0.8461538462a + a2 = 0 + -0.1025641026 0.8461538462a + a2 = 0 + -0.1025641026 Combine like terms: 0 + -0.1025641026 = -0.1025641026 0.8461538462a + a2 = -0.1025641026 The a term is 0.8461538462a. Take half its coefficient (0.4230769231). Square it (0.1789940829) and add it to both sides. Add '0.1789940829' to each side of the equation. 0.8461538462a + 0.1789940829 + a2 = -0.1025641026 + 0.1789940829 Reorder the terms: 0.1789940829 + 0.8461538462a + a2 = -0.1025641026 + 0.1789940829 Combine like terms: -0.1025641026 + 0.1789940829 = 0.0764299803 0.1789940829 + 0.8461538462a + a2 = 0.0764299803 Factor a perfect square on the left side: (a + 0.4230769231)(a + 0.4230769231) = 0.0764299803 Calculate the square root of the right side: 0.276459726 Break this problem into two subproblems by setting (a + 0.4230769231) equal to 0.276459726 and -0.276459726.Subproblem 1
a + 0.4230769231 = 0.276459726 Simplifying a + 0.4230769231 = 0.276459726 Reorder the terms: 0.4230769231 + a = 0.276459726 Solving 0.4230769231 + a = 0.276459726 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4230769231' to each side of the equation. 0.4230769231 + -0.4230769231 + a = 0.276459726 + -0.4230769231 Combine like terms: 0.4230769231 + -0.4230769231 = 0.0000000000 0.0000000000 + a = 0.276459726 + -0.4230769231 a = 0.276459726 + -0.4230769231 Combine like terms: 0.276459726 + -0.4230769231 = -0.1466171971 a = -0.1466171971 Simplifying a = -0.1466171971Subproblem 2
a + 0.4230769231 = -0.276459726 Simplifying a + 0.4230769231 = -0.276459726 Reorder the terms: 0.4230769231 + a = -0.276459726 Solving 0.4230769231 + a = -0.276459726 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4230769231' to each side of the equation. 0.4230769231 + -0.4230769231 + a = -0.276459726 + -0.4230769231 Combine like terms: 0.4230769231 + -0.4230769231 = 0.0000000000 0.0000000000 + a = -0.276459726 + -0.4230769231 a = -0.276459726 + -0.4230769231 Combine like terms: -0.276459726 + -0.4230769231 = -0.6995366491 a = -0.6995366491 Simplifying a = -0.6995366491Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.1466171971, -0.6995366491}
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