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Simplifying n2 + -14n + -49 = 0 Reorder the terms: -49 + -14n + n2 = 0 Solving -49 + -14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -14n + 49 + n2 = 0 + 49 Reorder the terms: -49 + 49 + -14n + n2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -14n + n2 = 0 + 49 -14n + n2 = 0 + 49 Combine like terms: 0 + 49 = 49 -14n + n2 = 49 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 = 49 + 49 Reorder the terms: 49 + -14n + n2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + -14n + n2 = 98 Factor a perfect square on the left side: (n + -7)(n + -7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (n + -7) equal to 9.899494937 and -9.899494937.Subproblem 1
n + -7 = 9.899494937 Simplifying n + -7 = 9.899494937 Reorder the terms: -7 + n = 9.899494937 Solving -7 + n = 9.899494937 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 = 9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + n = 9.899494937 + 7 n = 9.899494937 + 7 Combine like terms: 9.899494937 + 7 = 16.899494937 n = 16.899494937 Simplifying n = 16.899494937Subproblem 2
n + -7 = -9.899494937 Simplifying n + -7 = -9.899494937 Reorder the terms: -7 + n = -9.899494937 Solving -7 + n = -9.899494937 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 = -9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + n = -9.899494937 + 7 n = -9.899494937 + 7 Combine like terms: -9.899494937 + 7 = -2.899494937 n = -2.899494937 Simplifying n = -2.899494937Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.899494937, -2.899494937}
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