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Simplifying n2 + 16n = 28 Reorder the terms: 16n + n2 = 28 Solving 16n + n2 = 28 Solving for variable 'n'. Reorder the terms: -28 + 16n + n2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 16n + 28 + n2 = 0 + 28 Reorder the terms: -28 + 28 + 16n + n2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 16n + n2 = 0 + 28 16n + n2 = 0 + 28 Combine like terms: 0 + 28 = 28 16n + n2 = 28 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 = 28 + 64 Reorder the terms: 64 + 16n + n2 = 28 + 64 Combine like terms: 28 + 64 = 92 64 + 16n + n2 = 92 Factor a perfect square on the left side: (n + 8)(n + 8) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (n + 8) equal to 9.591663047 and -9.591663047.Subproblem 1
n + 8 = 9.591663047 Simplifying n + 8 = 9.591663047 Reorder the terms: 8 + n = 9.591663047 Solving 8 + n = 9.591663047 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 = 9.591663047 + -8 Combine like terms: 8 + -8 = 0 0 + n = 9.591663047 + -8 n = 9.591663047 + -8 Combine like terms: 9.591663047 + -8 = 1.591663047 n = 1.591663047 Simplifying n = 1.591663047Subproblem 2
n + 8 = -9.591663047 Simplifying n + 8 = -9.591663047 Reorder the terms: 8 + n = -9.591663047 Solving 8 + n = -9.591663047 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 = -9.591663047 + -8 Combine like terms: 8 + -8 = 0 0 + n = -9.591663047 + -8 n = -9.591663047 + -8 Combine like terms: -9.591663047 + -8 = -17.591663047 n = -17.591663047 Simplifying n = -17.591663047Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.591663047, -17.591663047}
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