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Simplifying n2 = -14n + -37 Reorder the terms: n2 = -37 + -14n Solving n2 = -37 + -14n Solving for variable 'n'. Reorder the terms: 37 + 14n + n2 = -37 + -14n + 37 + 14n Reorder the terms: 37 + 14n + n2 = -37 + 37 + -14n + 14n Combine like terms: -37 + 37 = 0 37 + 14n + n2 = 0 + -14n + 14n 37 + 14n + n2 = -14n + 14n Combine like terms: -14n + 14n = 0 37 + 14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 14n + -37 + n2 = 0 + -37 Reorder the terms: 37 + -37 + 14n + n2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 14n + n2 = 0 + -37 14n + n2 = 0 + -37 Combine like terms: 0 + -37 = -37 14n + n2 = -37 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 = -37 + 49 Reorder the terms: 49 + 14n + n2 = -37 + 49 Combine like terms: -37 + 49 = 12 49 + 14n + n2 = 12 Factor a perfect square on the left side: (n + 7)(n + 7) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (n + 7) equal to 3.464101615 and -3.464101615.Subproblem 1
n + 7 = 3.464101615 Simplifying n + 7 = 3.464101615 Reorder the terms: 7 + n = 3.464101615 Solving 7 + n = 3.464101615 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 = 3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + n = 3.464101615 + -7 n = 3.464101615 + -7 Combine like terms: 3.464101615 + -7 = -3.535898385 n = -3.535898385 Simplifying n = -3.535898385Subproblem 2
n + 7 = -3.464101615 Simplifying n + 7 = -3.464101615 Reorder the terms: 7 + n = -3.464101615 Solving 7 + n = -3.464101615 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 = -3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + n = -3.464101615 + -7 n = -3.464101615 + -7 Combine like terms: -3.464101615 + -7 = -10.464101615 n = -10.464101615 Simplifying n = -10.464101615Solution
The solution to the problem is based on the solutions from the subproblems. n = {-3.535898385, -10.464101615}
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