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Simplifying A2 + -1A + -14 = A Reorder the terms: -14 + -1A + A2 = A Solving -14 + -1A + A2 = A Solving for variable 'A'. Reorder the terms: -14 + -1A + -1A + A2 = A + -1A Combine like terms: -1A + -1A = -2A -14 + -2A + A2 = A + -1A Combine like terms: A + -1A = 0 -14 + -2A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -2A + 14 + A2 = 0 + 14 Reorder the terms: -14 + 14 + -2A + A2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2A + A2 = 0 + 14 -2A + A2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2A + A2 = 14 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 = 14 + 1 Reorder the terms: 1 + -2A + A2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + -2A + A2 = 15 Factor a perfect square on the left side: (A + -1)(A + -1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (A + -1) equal to 3.872983346 and -3.872983346.Subproblem 1
A + -1 = 3.872983346 Simplifying A + -1 = 3.872983346 Reorder the terms: -1 + A = 3.872983346 Solving -1 + A = 3.872983346 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 = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + A = 3.872983346 + 1 A = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 A = 4.872983346 Simplifying A = 4.872983346Subproblem 2
A + -1 = -3.872983346 Simplifying A + -1 = -3.872983346 Reorder the terms: -1 + A = -3.872983346 Solving -1 + A = -3.872983346 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 = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + A = -3.872983346 + 1 A = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 A = -2.872983346 Simplifying A = -2.872983346Solution
The solution to the problem is based on the solutions from the subproblems. A = {4.872983346, -2.872983346}
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