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Simplifying 2A2 + -16A + 64 = 36 Reorder the terms: 64 + -16A + 2A2 = 36 Solving 64 + -16A + 2A2 = 36 Solving for variable 'A'. Reorder the terms: 64 + -36 + -16A + 2A2 = 36 + -36 Combine like terms: 64 + -36 = 28 28 + -16A + 2A2 = 36 + -36 Combine like terms: 36 + -36 = 0 28 + -16A + 2A2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -8A + A2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -8A + A2)' equal to zero and attempt to solve: Simplifying 14 + -8A + A2 = 0 Solving 14 + -8A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8A + -14 + A2 = 0 + -14 Reorder the terms: 14 + -14 + -8A + A2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8A + A2 = 0 + -14 -8A + A2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8A + A2 = -14 The A term is -8A. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8A + 16 + A2 = -14 + 16 Reorder the terms: 16 + -8A + A2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8A + A2 = 2 Factor a perfect square on the left side: (A + -4)(A + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (A + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
A + -4 = 1.414213562 Simplifying A + -4 = 1.414213562 Reorder the terms: -4 + A = 1.414213562 Solving -4 + A = 1.414213562 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + A = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + A = 1.414213562 + 4 A = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 A = 5.414213562 Simplifying A = 5.414213562Subproblem 2
A + -4 = -1.414213562 Simplifying A + -4 = -1.414213562 Reorder the terms: -4 + A = -1.414213562 Solving -4 + A = -1.414213562 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + A = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + A = -1.414213562 + 4 A = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 A = 2.585786438 Simplifying A = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. A = {5.414213562, 2.585786438}Solution
A = {5.414213562, 2.585786438}
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