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Simplifying n2 + -16n = 64 Reorder the terms: -16n + n2 = 64 Solving -16n + n2 = 64 Solving for variable 'n'. Reorder the terms: -64 + -16n + n2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -16n + 64 + n2 = 0 + 64 Reorder the terms: -64 + 64 + -16n + n2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -16n + n2 = 0 + 64 -16n + n2 = 0 + 64 Combine like terms: 0 + 64 = 64 -16n + n2 = 64 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 = 64 + 64 Reorder the terms: 64 + -16n + n2 = 64 + 64 Combine like terms: 64 + 64 = 128 64 + -16n + n2 = 128 Factor a perfect square on the left side: (n + -8)(n + -8) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (n + -8) equal to 11.313708499 and -11.313708499.Subproblem 1
n + -8 = 11.313708499 Simplifying n + -8 = 11.313708499 Reorder the terms: -8 + n = 11.313708499 Solving -8 + n = 11.313708499 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 = 11.313708499 + 8 Combine like terms: -8 + 8 = 0 0 + n = 11.313708499 + 8 n = 11.313708499 + 8 Combine like terms: 11.313708499 + 8 = 19.313708499 n = 19.313708499 Simplifying n = 19.313708499Subproblem 2
n + -8 = -11.313708499 Simplifying n + -8 = -11.313708499 Reorder the terms: -8 + n = -11.313708499 Solving -8 + n = -11.313708499 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 = -11.313708499 + 8 Combine like terms: -8 + 8 = 0 0 + n = -11.313708499 + 8 n = -11.313708499 + 8 Combine like terms: -11.313708499 + 8 = -3.313708499 n = -3.313708499 Simplifying n = -3.313708499Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.313708499, -3.313708499}
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