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Simplifying A2 + 2A + 2 + -1 = 167 Reorder the terms: 2 + -1 + 2A + A2 = 167 Combine like terms: 2 + -1 = 1 1 + 2A + A2 = 167 Solving 1 + 2A + A2 = 167 Solving for variable 'A'. Reorder the terms: 1 + -167 + 2A + A2 = 167 + -167 Combine like terms: 1 + -167 = -166 -166 + 2A + A2 = 167 + -167 Combine like terms: 167 + -167 = 0 -166 + 2A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + 2A + 166 + A2 = 0 + 166 Reorder the terms: -166 + 166 + 2A + A2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + 2A + A2 = 0 + 166 2A + A2 = 0 + 166 Combine like terms: 0 + 166 = 166 2A + A2 = 166 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 = 166 + 1 Reorder the terms: 1 + 2A + A2 = 166 + 1 Combine like terms: 166 + 1 = 167 1 + 2A + A2 = 167 Factor a perfect square on the left side: (A + 1)(A + 1) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (A + 1) equal to 12.922847983 and -12.922847983.Subproblem 1
A + 1 = 12.922847983 Simplifying A + 1 = 12.922847983 Reorder the terms: 1 + A = 12.922847983 Solving 1 + A = 12.922847983 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 = 12.922847983 + -1 Combine like terms: 1 + -1 = 0 0 + A = 12.922847983 + -1 A = 12.922847983 + -1 Combine like terms: 12.922847983 + -1 = 11.922847983 A = 11.922847983 Simplifying A = 11.922847983Subproblem 2
A + 1 = -12.922847983 Simplifying A + 1 = -12.922847983 Reorder the terms: 1 + A = -12.922847983 Solving 1 + A = -12.922847983 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 = -12.922847983 + -1 Combine like terms: 1 + -1 = 0 0 + A = -12.922847983 + -1 A = -12.922847983 + -1 Combine like terms: -12.922847983 + -1 = -13.922847983 A = -13.922847983 Simplifying A = -13.922847983Solution
The solution to the problem is based on the solutions from the subproblems. A = {11.922847983, -13.922847983}
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