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Simplifying n2 + 16n + -19 = 0 Reorder the terms: -19 + 16n + n2 = 0 Solving -19 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 16n + 19 + n2 = 0 + 19 Reorder the terms: -19 + 19 + 16n + n2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 16n + n2 = 0 + 19 16n + n2 = 0 + 19 Combine like terms: 0 + 19 = 19 16n + n2 = 19 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 = 19 + 64 Reorder the terms: 64 + 16n + n2 = 19 + 64 Combine like terms: 19 + 64 = 83 64 + 16n + n2 = 83 Factor a perfect square on the left side: (n + 8)(n + 8) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (n + 8) equal to 9.110433579 and -9.110433579.Subproblem 1
n + 8 = 9.110433579 Simplifying n + 8 = 9.110433579 Reorder the terms: 8 + n = 9.110433579 Solving 8 + n = 9.110433579 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 = 9.110433579 + -8 Combine like terms: 8 + -8 = 0 0 + n = 9.110433579 + -8 n = 9.110433579 + -8 Combine like terms: 9.110433579 + -8 = 1.110433579 n = 1.110433579 Simplifying n = 1.110433579Subproblem 2
n + 8 = -9.110433579 Simplifying n + 8 = -9.110433579 Reorder the terms: 8 + n = -9.110433579 Solving 8 + n = -9.110433579 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 = -9.110433579 + -8 Combine like terms: 8 + -8 = 0 0 + n = -9.110433579 + -8 n = -9.110433579 + -8 Combine like terms: -9.110433579 + -8 = -17.110433579 n = -17.110433579 Simplifying n = -17.110433579Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.110433579, -17.110433579}
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