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Simplifying 2A + A2 = 0.1 Solving 2A + A2 = 0.1 Solving for variable 'A'. Reorder the terms: -0.1 + 2A + A2 = 0.1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 -0.1 + 2A + A2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 2A + 0.1 + A2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 2A + A2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 2A + A2 = 0.0 + 0.1 2A + A2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 2A + A2 = 0.1 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 = 0.1 + 1 Reorder the terms: 1 + 2A + A2 = 0.1 + 1 Combine like terms: 0.1 + 1 = 1.1 1 + 2A + A2 = 1.1 Factor a perfect square on the left side: (A + 1)(A + 1) = 1.1 Calculate the square root of the right side: 1.048808848 Break this problem into two subproblems by setting (A + 1) equal to 1.048808848 and -1.048808848.Subproblem 1
A + 1 = 1.048808848 Simplifying A + 1 = 1.048808848 Reorder the terms: 1 + A = 1.048808848 Solving 1 + A = 1.048808848 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 = 1.048808848 + -1 Combine like terms: 1 + -1 = 0 0 + A = 1.048808848 + -1 A = 1.048808848 + -1 Combine like terms: 1.048808848 + -1 = 0.048808848 A = 0.048808848 Simplifying A = 0.048808848Subproblem 2
A + 1 = -1.048808848 Simplifying A + 1 = -1.048808848 Reorder the terms: 1 + A = -1.048808848 Solving 1 + A = -1.048808848 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 = -1.048808848 + -1 Combine like terms: 1 + -1 = 0 0 + A = -1.048808848 + -1 A = -1.048808848 + -1 Combine like terms: -1.048808848 + -1 = -2.048808848 A = -2.048808848 Simplifying A = -2.048808848Solution
The solution to the problem is based on the solutions from the subproblems. A = {0.048808848, -2.048808848}
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