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Simplifying n2 + 14n + -29 = -2 Reorder the terms: -29 + 14n + n2 = -2 Solving -29 + 14n + n2 = -2 Solving for variable 'n'. Reorder the terms: -29 + 2 + 14n + n2 = -2 + 2 Combine like terms: -29 + 2 = -27 -27 + 14n + n2 = -2 + 2 Combine like terms: -2 + 2 = 0 -27 + 14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 14n + 27 + n2 = 0 + 27 Reorder the terms: -27 + 27 + 14n + n2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 14n + n2 = 0 + 27 14n + n2 = 0 + 27 Combine like terms: 0 + 27 = 27 14n + n2 = 27 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 = 27 + 49 Reorder the terms: 49 + 14n + n2 = 27 + 49 Combine like terms: 27 + 49 = 76 49 + 14n + n2 = 76 Factor a perfect square on the left side: (n + 7)(n + 7) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (n + 7) equal to 8.717797887 and -8.717797887.Subproblem 1
n + 7 = 8.717797887 Simplifying n + 7 = 8.717797887 Reorder the terms: 7 + n = 8.717797887 Solving 7 + n = 8.717797887 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 = 8.717797887 + -7 Combine like terms: 7 + -7 = 0 0 + n = 8.717797887 + -7 n = 8.717797887 + -7 Combine like terms: 8.717797887 + -7 = 1.717797887 n = 1.717797887 Simplifying n = 1.717797887Subproblem 2
n + 7 = -8.717797887 Simplifying n + 7 = -8.717797887 Reorder the terms: 7 + n = -8.717797887 Solving 7 + n = -8.717797887 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 = -8.717797887 + -7 Combine like terms: 7 + -7 = 0 0 + n = -8.717797887 + -7 n = -8.717797887 + -7 Combine like terms: -8.717797887 + -7 = -15.717797887 n = -15.717797887 Simplifying n = -15.717797887Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.717797887, -15.717797887}
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