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Simplifying N2 + -16N + 32 = 0 Reorder the terms: 32 + -16N + N2 = 0 Solving 32 + -16N + N2 = 0 Solving for variable 'N'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -16N + -32 + N2 = 0 + -32 Reorder the terms: 32 + -32 + -16N + N2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -16N + N2 = 0 + -32 -16N + N2 = 0 + -32 Combine like terms: 0 + -32 = -32 -16N + N2 = -32 The N term is -16N. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16N + 64 + N2 = -32 + 64 Reorder the terms: 64 + -16N + N2 = -32 + 64 Combine like terms: -32 + 64 = 32 64 + -16N + N2 = 32 Factor a perfect square on the left side: (N + -8)(N + -8) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (N + -8) equal to 5.656854249 and -5.656854249.Subproblem 1
N + -8 = 5.656854249 Simplifying N + -8 = 5.656854249 Reorder the terms: -8 + N = 5.656854249 Solving -8 + N = 5.656854249 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + N = 5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + N = 5.656854249 + 8 N = 5.656854249 + 8 Combine like terms: 5.656854249 + 8 = 13.656854249 N = 13.656854249 Simplifying N = 13.656854249Subproblem 2
N + -8 = -5.656854249 Simplifying N + -8 = -5.656854249 Reorder the terms: -8 + N = -5.656854249 Solving -8 + N = -5.656854249 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + N = -5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + N = -5.656854249 + 8 N = -5.656854249 + 8 Combine like terms: -5.656854249 + 8 = 2.343145751 N = 2.343145751 Simplifying N = 2.343145751Solution
The solution to the problem is based on the solutions from the subproblems. N = {13.656854249, 2.343145751}
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