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Simplifying n2 + 16n = 117 Reorder the terms: 16n + n2 = 117 Solving 16n + n2 = 117 Solving for variable 'n'. Reorder the terms: -117 + 16n + n2 = 117 + -117 Combine like terms: 117 + -117 = 0 -117 + 16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + 16n + 117 + n2 = 0 + 117 Reorder the terms: -117 + 117 + 16n + n2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + 16n + n2 = 0 + 117 16n + n2 = 0 + 117 Combine like terms: 0 + 117 = 117 16n + n2 = 117 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 = 117 + 64 Reorder the terms: 64 + 16n + n2 = 117 + 64 Combine like terms: 117 + 64 = 181 64 + 16n + n2 = 181 Factor a perfect square on the left side: (n + 8)(n + 8) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (n + 8) equal to 13.453624047 and -13.453624047.Subproblem 1
n + 8 = 13.453624047 Simplifying n + 8 = 13.453624047 Reorder the terms: 8 + n = 13.453624047 Solving 8 + n = 13.453624047 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 = 13.453624047 + -8 Combine like terms: 8 + -8 = 0 0 + n = 13.453624047 + -8 n = 13.453624047 + -8 Combine like terms: 13.453624047 + -8 = 5.453624047 n = 5.453624047 Simplifying n = 5.453624047Subproblem 2
n + 8 = -13.453624047 Simplifying n + 8 = -13.453624047 Reorder the terms: 8 + n = -13.453624047 Solving 8 + n = -13.453624047 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 = -13.453624047 + -8 Combine like terms: 8 + -8 = 0 0 + n = -13.453624047 + -8 n = -13.453624047 + -8 Combine like terms: -13.453624047 + -8 = -21.453624047 n = -21.453624047 Simplifying n = -21.453624047Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.453624047, -21.453624047}
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