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Simplifying n2 + -14n + 35 = 0 Reorder the terms: 35 + -14n + n2 = 0 Solving 35 + -14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -14n + -35 + n2 = 0 + -35 Reorder the terms: 35 + -35 + -14n + n2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -14n + n2 = 0 + -35 -14n + n2 = 0 + -35 Combine like terms: 0 + -35 = -35 -14n + n2 = -35 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 = -35 + 49 Reorder the terms: 49 + -14n + n2 = -35 + 49 Combine like terms: -35 + 49 = 14 49 + -14n + n2 = 14 Factor a perfect square on the left side: (n + -7)(n + -7) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (n + -7) equal to 3.741657387 and -3.741657387.Subproblem 1
n + -7 = 3.741657387 Simplifying n + -7 = 3.741657387 Reorder the terms: -7 + n = 3.741657387 Solving -7 + n = 3.741657387 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 = 3.741657387 + 7 Combine like terms: -7 + 7 = 0 0 + n = 3.741657387 + 7 n = 3.741657387 + 7 Combine like terms: 3.741657387 + 7 = 10.741657387 n = 10.741657387 Simplifying n = 10.741657387Subproblem 2
n + -7 = -3.741657387 Simplifying n + -7 = -3.741657387 Reorder the terms: -7 + n = -3.741657387 Solving -7 + n = -3.741657387 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 = -3.741657387 + 7 Combine like terms: -7 + 7 = 0 0 + n = -3.741657387 + 7 n = -3.741657387 + 7 Combine like terms: -3.741657387 + 7 = 3.258342613 n = 3.258342613 Simplifying n = 3.258342613Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.741657387, 3.258342613}
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