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Simplifying (A + -2)(A + 1) = 3A2 + -4 Reorder the terms: (-2 + A)(A + 1) = 3A2 + -4 Reorder the terms: (-2 + A)(1 + A) = 3A2 + -4 Multiply (-2 + A) * (1 + A) (-2(1 + A) + A(1 + A)) = 3A2 + -4 ((1 * -2 + A * -2) + A(1 + A)) = 3A2 + -4 ((-2 + -2A) + A(1 + A)) = 3A2 + -4 (-2 + -2A + (1 * A + A * A)) = 3A2 + -4 (-2 + -2A + (1A + A2)) = 3A2 + -4 Combine like terms: -2A + 1A = -1A (-2 + -1A + A2) = 3A2 + -4 Reorder the terms: -2 + -1A + A2 = -4 + 3A2 Solving -2 + -1A + A2 = -4 + 3A2 Solving for variable 'A'. Reorder the terms: -2 + 4 + -1A + A2 + -3A2 = -4 + 3A2 + 4 + -3A2 Combine like terms: -2 + 4 = 2 2 + -1A + A2 + -3A2 = -4 + 3A2 + 4 + -3A2 Combine like terms: A2 + -3A2 = -2A2 2 + -1A + -2A2 = -4 + 3A2 + 4 + -3A2 Reorder the terms: 2 + -1A + -2A2 = -4 + 4 + 3A2 + -3A2 Combine like terms: -4 + 4 = 0 2 + -1A + -2A2 = 0 + 3A2 + -3A2 2 + -1A + -2A2 = 3A2 + -3A2 Combine like terms: 3A2 + -3A2 = 0 2 + -1A + -2A2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + 0.5A + A2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.5A + 1 + A2 = 0 + 1 Reorder the terms: -1 + 1 + 0.5A + A2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.5A + A2 = 0 + 1 0.5A + A2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.5A + A2 = 1 The A term is 0.5A. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5A + 0.0625 + A2 = 1 + 0.0625 Reorder the terms: 0.0625 + 0.5A + A2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + 0.5A + A2 = 1.0625 Factor a perfect square on the left side: (A + 0.25)(A + 0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (A + 0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
A + 0.25 = 1.030776406 Simplifying A + 0.25 = 1.030776406 Reorder the terms: 0.25 + A = 1.030776406 Solving 0.25 + A = 1.030776406 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + A = 1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + A = 1.030776406 + -0.25 A = 1.030776406 + -0.25 Combine like terms: 1.030776406 + -0.25 = 0.780776406 A = 0.780776406 Simplifying A = 0.780776406Subproblem 2
A + 0.25 = -1.030776406 Simplifying A + 0.25 = -1.030776406 Reorder the terms: 0.25 + A = -1.030776406 Solving 0.25 + A = -1.030776406 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + A = -1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + A = -1.030776406 + -0.25 A = -1.030776406 + -0.25 Combine like terms: -1.030776406 + -0.25 = -1.280776406 A = -1.280776406 Simplifying A = -1.280776406Solution
The solution to the problem is based on the solutions from the subproblems. A = {0.780776406, -1.280776406}
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