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Simplifying n2 + -14n + 7 = 0 Reorder the terms: 7 + -14n + n2 = 0 Solving 7 + -14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -14n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + -14n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -14n + n2 = 0 + -7 -14n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -14n + n2 = -7 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 = -7 + 49 Reorder the terms: 49 + -14n + n2 = -7 + 49 Combine like terms: -7 + 49 = 42 49 + -14n + n2 = 42 Factor a perfect square on the left side: (n + -7)(n + -7) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (n + -7) equal to 6.480740698 and -6.480740698.Subproblem 1
n + -7 = 6.480740698 Simplifying n + -7 = 6.480740698 Reorder the terms: -7 + n = 6.480740698 Solving -7 + n = 6.480740698 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 = 6.480740698 + 7 Combine like terms: -7 + 7 = 0 0 + n = 6.480740698 + 7 n = 6.480740698 + 7 Combine like terms: 6.480740698 + 7 = 13.480740698 n = 13.480740698 Simplifying n = 13.480740698Subproblem 2
n + -7 = -6.480740698 Simplifying n + -7 = -6.480740698 Reorder the terms: -7 + n = -6.480740698 Solving -7 + n = -6.480740698 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 = -6.480740698 + 7 Combine like terms: -7 + 7 = 0 0 + n = -6.480740698 + 7 n = -6.480740698 + 7 Combine like terms: -6.480740698 + 7 = 0.519259302 n = 0.519259302 Simplifying n = 0.519259302Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.480740698, 0.519259302}
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