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Simplifying A2 + 11A = 121 Reorder the terms: 11A + A2 = 121 Solving 11A + A2 = 121 Solving for variable 'A'. Reorder the terms: -121 + 11A + A2 = 121 + -121 Combine like terms: 121 + -121 = 0 -121 + 11A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + 11A + 121 + A2 = 0 + 121 Reorder the terms: -121 + 121 + 11A + A2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 11A + A2 = 0 + 121 11A + A2 = 0 + 121 Combine like terms: 0 + 121 = 121 11A + A2 = 121 The A term is 11A. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11A + 30.25 + A2 = 121 + 30.25 Reorder the terms: 30.25 + 11A + A2 = 121 + 30.25 Combine like terms: 121 + 30.25 = 151.25 30.25 + 11A + A2 = 151.25 Factor a perfect square on the left side: (A + 5.5)(A + 5.5) = 151.25 Calculate the square root of the right side: 12.298373876 Break this problem into two subproblems by setting (A + 5.5) equal to 12.298373876 and -12.298373876.Subproblem 1
A + 5.5 = 12.298373876 Simplifying A + 5.5 = 12.298373876 Reorder the terms: 5.5 + A = 12.298373876 Solving 5.5 + A = 12.298373876 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + A = 12.298373876 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + A = 12.298373876 + -5.5 A = 12.298373876 + -5.5 Combine like terms: 12.298373876 + -5.5 = 6.798373876 A = 6.798373876 Simplifying A = 6.798373876Subproblem 2
A + 5.5 = -12.298373876 Simplifying A + 5.5 = -12.298373876 Reorder the terms: 5.5 + A = -12.298373876 Solving 5.5 + A = -12.298373876 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + A = -12.298373876 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + A = -12.298373876 + -5.5 A = -12.298373876 + -5.5 Combine like terms: -12.298373876 + -5.5 = -17.798373876 A = -17.798373876 Simplifying A = -17.798373876Solution
The solution to the problem is based on the solutions from the subproblems. A = {6.798373876, -17.798373876}
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