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Simplifying A2 + -16A + 32 = 0 Reorder the terms: 32 + -16A + A2 = 0 Solving 32 + -16A + A2 = 0 Solving for variable 'A'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -16A + -32 + A2 = 0 + -32 Reorder the terms: 32 + -32 + -16A + A2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -16A + A2 = 0 + -32 -16A + A2 = 0 + -32 Combine like terms: 0 + -32 = -32 -16A + A2 = -32 The A term is -16A. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16A + 64 + A2 = -32 + 64 Reorder the terms: 64 + -16A + A2 = -32 + 64 Combine like terms: -32 + 64 = 32 64 + -16A + A2 = 32 Factor a perfect square on the left side: (A + -8)(A + -8) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (A + -8) equal to 5.656854249 and -5.656854249.Subproblem 1
A + -8 = 5.656854249 Simplifying A + -8 = 5.656854249 Reorder the terms: -8 + A = 5.656854249 Solving -8 + A = 5.656854249 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + A = 5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + A = 5.656854249 + 8 A = 5.656854249 + 8 Combine like terms: 5.656854249 + 8 = 13.656854249 A = 13.656854249 Simplifying A = 13.656854249Subproblem 2
A + -8 = -5.656854249 Simplifying A + -8 = -5.656854249 Reorder the terms: -8 + A = -5.656854249 Solving -8 + A = -5.656854249 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + A = -5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + A = -5.656854249 + 8 A = -5.656854249 + 8 Combine like terms: -5.656854249 + 8 = 2.343145751 A = 2.343145751 Simplifying A = 2.343145751Solution
The solution to the problem is based on the solutions from the subproblems. A = {13.656854249, 2.343145751}
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