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Simplifying a2 + 12742a = 1225 Reorder the terms: 12742a + a2 = 1225 Solving 12742a + a2 = 1225 Solving for variable 'a'. Reorder the terms: -1225 + 12742a + a2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1225 + 12742a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '1225' to each side of the equation. -1225 + 12742a + 1225 + a2 = 0 + 1225 Reorder the terms: -1225 + 1225 + 12742a + a2 = 0 + 1225 Combine like terms: -1225 + 1225 = 0 0 + 12742a + a2 = 0 + 1225 12742a + a2 = 0 + 1225 Combine like terms: 0 + 1225 = 1225 12742a + a2 = 1225 The a term is 12742a. Take half its coefficient (6371). Square it (40589641) and add it to both sides. Add '40589641' to each side of the equation. 12742a + 40589641 + a2 = 1225 + 40589641 Reorder the terms: 40589641 + 12742a + a2 = 1225 + 40589641 Combine like terms: 1225 + 40589641 = 40590866 40589641 + 12742a + a2 = 40590866 Factor a perfect square on the left side: (a + 6371)(a + 6371) = 40590866 Calculate the square root of the right side: 6371.096138028 Break this problem into two subproblems by setting (a + 6371) equal to 6371.096138028 and -6371.096138028.Subproblem 1
a + 6371 = 6371.096138028 Simplifying a + 6371 = 6371.096138028 Reorder the terms: 6371 + a = 6371.096138028 Solving 6371 + a = 6371.096138028 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6371' to each side of the equation. 6371 + -6371 + a = 6371.096138028 + -6371 Combine like terms: 6371 + -6371 = 0 0 + a = 6371.096138028 + -6371 a = 6371.096138028 + -6371 Combine like terms: 6371.096138028 + -6371 = 0.096138028 a = 0.096138028 Simplifying a = 0.096138028Subproblem 2
a + 6371 = -6371.096138028 Simplifying a + 6371 = -6371.096138028 Reorder the terms: 6371 + a = -6371.096138028 Solving 6371 + a = -6371.096138028 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6371' to each side of the equation. 6371 + -6371 + a = -6371.096138028 + -6371 Combine like terms: 6371 + -6371 = 0 0 + a = -6371.096138028 + -6371 a = -6371.096138028 + -6371 Combine like terms: -6371.096138028 + -6371 = -12742.096138028 a = -12742.096138028 Simplifying a = -12742.096138028Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.096138028, -12742.096138028}
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