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Simplifying n2 + 14n + -34 = 0 Reorder the terms: -34 + 14n + n2 = 0 Solving -34 + 14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 14n + 34 + n2 = 0 + 34 Reorder the terms: -34 + 34 + 14n + n2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 14n + n2 = 0 + 34 14n + n2 = 0 + 34 Combine like terms: 0 + 34 = 34 14n + n2 = 34 The n term is 14n. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14n + 49 + n2 = 34 + 49 Reorder the terms: 49 + 14n + n2 = 34 + 49 Combine like terms: 34 + 49 = 83 49 + 14n + n2 = 83 Factor a perfect square on the left side: (n + 7)(n + 7) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (n + 7) equal to 9.110433579 and -9.110433579.Subproblem 1
n + 7 = 9.110433579 Simplifying n + 7 = 9.110433579 Reorder the terms: 7 + n = 9.110433579 Solving 7 + n = 9.110433579 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 9.110433579 + -7 Combine like terms: 7 + -7 = 0 0 + n = 9.110433579 + -7 n = 9.110433579 + -7 Combine like terms: 9.110433579 + -7 = 2.110433579 n = 2.110433579 Simplifying n = 2.110433579Subproblem 2
n + 7 = -9.110433579 Simplifying n + 7 = -9.110433579 Reorder the terms: 7 + n = -9.110433579 Solving 7 + n = -9.110433579 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = -9.110433579 + -7 Combine like terms: 7 + -7 = 0 0 + n = -9.110433579 + -7 n = -9.110433579 + -7 Combine like terms: -9.110433579 + -7 = -16.110433579 n = -16.110433579 Simplifying n = -16.110433579Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.110433579, -16.110433579}
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