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Simplifying n2 + n + -11 = 0 Reorder the terms: -11 + n + n2 = 0 Solving -11 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + n + 11 + n2 = 0 + 11 Reorder the terms: -11 + 11 + n + n2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + n + n2 = 0 + 11 n + n2 = 0 + 11 Combine like terms: 0 + 11 = 11 n + n2 = 11 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 11 + 0.25 Reorder the terms: 0.25 + n + n2 = 11 + 0.25 Combine like terms: 11 + 0.25 = 11.25 0.25 + n + n2 = 11.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (n + 0.5) equal to 3.354101966 and -3.354101966.Subproblem 1
n + 0.5 = 3.354101966 Simplifying n + 0.5 = 3.354101966 Reorder the terms: 0.5 + n = 3.354101966 Solving 0.5 + n = 3.354101966 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 3.354101966 + -0.5 n = 3.354101966 + -0.5 Combine like terms: 3.354101966 + -0.5 = 2.854101966 n = 2.854101966 Simplifying n = 2.854101966Subproblem 2
n + 0.5 = -3.354101966 Simplifying n + 0.5 = -3.354101966 Reorder the terms: 0.5 + n = -3.354101966 Solving 0.5 + n = -3.354101966 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -3.354101966 + -0.5 n = -3.354101966 + -0.5 Combine like terms: -3.354101966 + -0.5 = -3.854101966 n = -3.854101966 Simplifying n = -3.854101966Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.854101966, -3.854101966}
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