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Simplifying (A + -8)(A + 2) = 2 Reorder the terms: (-8 + A)(A + 2) = 2 Reorder the terms: (-8 + A)(2 + A) = 2 Multiply (-8 + A) * (2 + A) (-8(2 + A) + A(2 + A)) = 2 ((2 * -8 + A * -8) + A(2 + A)) = 2 ((-16 + -8A) + A(2 + A)) = 2 (-16 + -8A + (2 * A + A * A)) = 2 (-16 + -8A + (2A + A2)) = 2 Combine like terms: -8A + 2A = -6A (-16 + -6A + A2) = 2 Solving -16 + -6A + A2 = 2 Solving for variable 'A'. Reorder the terms: -16 + -2 + -6A + A2 = 2 + -2 Combine like terms: -16 + -2 = -18 -18 + -6A + A2 = 2 + -2 Combine like terms: 2 + -2 = 0 -18 + -6A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6A + 18 + A2 = 0 + 18 Reorder the terms: -18 + 18 + -6A + A2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6A + A2 = 0 + 18 -6A + A2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6A + A2 = 18 The A term is -6A. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6A + 9 + A2 = 18 + 9 Reorder the terms: 9 + -6A + A2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6A + A2 = 27 Factor a perfect square on the left side: (A + -3)(A + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (A + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
A + -3 = 5.196152423 Simplifying A + -3 = 5.196152423 Reorder the terms: -3 + A = 5.196152423 Solving -3 + A = 5.196152423 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + A = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + A = 5.196152423 + 3 A = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 A = 8.196152423 Simplifying A = 8.196152423Subproblem 2
A + -3 = -5.196152423 Simplifying A + -3 = -5.196152423 Reorder the terms: -3 + A = -5.196152423 Solving -3 + A = -5.196152423 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + A = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + A = -5.196152423 + 3 A = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 A = -2.196152423 Simplifying A = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. A = {8.196152423, -2.196152423}
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