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Simplifying n2 + -6n + -89 = 0 Reorder the terms: -89 + -6n + n2 = 0 Solving -89 + -6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + -6n + 89 + n2 = 0 + 89 Reorder the terms: -89 + 89 + -6n + n2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + -6n + n2 = 0 + 89 -6n + n2 = 0 + 89 Combine like terms: 0 + 89 = 89 -6n + n2 = 89 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 89 + 9 Reorder the terms: 9 + -6n + n2 = 89 + 9 Combine like terms: 89 + 9 = 98 9 + -6n + n2 = 98 Factor a perfect square on the left side: (n + -3)(n + -3) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (n + -3) equal to 9.899494937 and -9.899494937.Subproblem 1
n + -3 = 9.899494937 Simplifying n + -3 = 9.899494937 Reorder the terms: -3 + n = 9.899494937 Solving -3 + n = 9.899494937 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 9.899494937 + 3 Combine like terms: -3 + 3 = 0 0 + n = 9.899494937 + 3 n = 9.899494937 + 3 Combine like terms: 9.899494937 + 3 = 12.899494937 n = 12.899494937 Simplifying n = 12.899494937Subproblem 2
n + -3 = -9.899494937 Simplifying n + -3 = -9.899494937 Reorder the terms: -3 + n = -9.899494937 Solving -3 + n = -9.899494937 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -9.899494937 + 3 Combine like terms: -3 + 3 = 0 0 + n = -9.899494937 + 3 n = -9.899494937 + 3 Combine like terms: -9.899494937 + 3 = -6.899494937 n = -6.899494937 Simplifying n = -6.899494937Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.899494937, -6.899494937}
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