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Simplifying A * A + 2A = 37250 Multiply A * A A2 + 2A = 37250 Reorder the terms: 2A + A2 = 37250 Solving 2A + A2 = 37250 Solving for variable 'A'. Reorder the terms: -37250 + 2A + A2 = 37250 + -37250 Combine like terms: 37250 + -37250 = 0 -37250 + 2A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '37250' to each side of the equation. -37250 + 2A + 37250 + A2 = 0 + 37250 Reorder the terms: -37250 + 37250 + 2A + A2 = 0 + 37250 Combine like terms: -37250 + 37250 = 0 0 + 2A + A2 = 0 + 37250 2A + A2 = 0 + 37250 Combine like terms: 0 + 37250 = 37250 2A + A2 = 37250 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 = 37250 + 1 Reorder the terms: 1 + 2A + A2 = 37250 + 1 Combine like terms: 37250 + 1 = 37251 1 + 2A + A2 = 37251 Factor a perfect square on the left side: (A + 1)(A + 1) = 37251 Calculate the square root of the right side: 193.005181278 Break this problem into two subproblems by setting (A + 1) equal to 193.005181278 and -193.005181278.Subproblem 1
A + 1 = 193.005181278 Simplifying A + 1 = 193.005181278 Reorder the terms: 1 + A = 193.005181278 Solving 1 + A = 193.005181278 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 = 193.005181278 + -1 Combine like terms: 1 + -1 = 0 0 + A = 193.005181278 + -1 A = 193.005181278 + -1 Combine like terms: 193.005181278 + -1 = 192.005181278 A = 192.005181278 Simplifying A = 192.005181278Subproblem 2
A + 1 = -193.005181278 Simplifying A + 1 = -193.005181278 Reorder the terms: 1 + A = -193.005181278 Solving 1 + A = -193.005181278 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 = -193.005181278 + -1 Combine like terms: 1 + -1 = 0 0 + A = -193.005181278 + -1 A = -193.005181278 + -1 Combine like terms: -193.005181278 + -1 = -194.005181278 A = -194.005181278 Simplifying A = -194.005181278Solution
The solution to the problem is based on the solutions from the subproblems. A = {192.005181278, -194.005181278}
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