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Simplifying A2 + (9 + 2A) = 10000 Remove parenthesis around (9 + 2A) A2 + 9 + 2A = 10000 Reorder the terms: 9 + 2A + A2 = 10000 Solving 9 + 2A + A2 = 10000 Solving for variable 'A'. Reorder the terms: 9 + -10000 + 2A + A2 = 10000 + -10000 Combine like terms: 9 + -10000 = -9991 -9991 + 2A + A2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 -9991 + 2A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '9991' to each side of the equation. -9991 + 2A + 9991 + A2 = 0 + 9991 Reorder the terms: -9991 + 9991 + 2A + A2 = 0 + 9991 Combine like terms: -9991 + 9991 = 0 0 + 2A + A2 = 0 + 9991 2A + A2 = 0 + 9991 Combine like terms: 0 + 9991 = 9991 2A + A2 = 9991 The A term is 2A. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2A + 1 + A2 = 9991 + 1 Reorder the terms: 1 + 2A + A2 = 9991 + 1 Combine like terms: 9991 + 1 = 9992 1 + 2A + A2 = 9992 Factor a perfect square on the left side: (A + 1)(A + 1) = 9992 Calculate the square root of the right side: 99.959991997 Break this problem into two subproblems by setting (A + 1) equal to 99.959991997 and -99.959991997.Subproblem 1
A + 1 = 99.959991997 Simplifying A + 1 = 99.959991997 Reorder the terms: 1 + A = 99.959991997 Solving 1 + A = 99.959991997 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + A = 99.959991997 + -1 Combine like terms: 1 + -1 = 0 0 + A = 99.959991997 + -1 A = 99.959991997 + -1 Combine like terms: 99.959991997 + -1 = 98.959991997 A = 98.959991997 Simplifying A = 98.959991997Subproblem 2
A + 1 = -99.959991997 Simplifying A + 1 = -99.959991997 Reorder the terms: 1 + A = -99.959991997 Solving 1 + A = -99.959991997 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + A = -99.959991997 + -1 Combine like terms: 1 + -1 = 0 0 + A = -99.959991997 + -1 A = -99.959991997 + -1 Combine like terms: -99.959991997 + -1 = -100.959991997 A = -100.959991997 Simplifying A = -100.959991997Solution
The solution to the problem is based on the solutions from the subproblems. A = {98.959991997, -100.959991997}
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