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Simplifying n2 + n + -360 = 0 Reorder the terms: -360 + n + n2 = 0 Solving -360 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + n + 360 + n2 = 0 + 360 Reorder the terms: -360 + 360 + n + n2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + n + n2 = 0 + 360 n + n2 = 0 + 360 Combine like terms: 0 + 360 = 360 n + n2 = 360 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 = 360 + 0.25 Reorder the terms: 0.25 + n + n2 = 360 + 0.25 Combine like terms: 360 + 0.25 = 360.25 0.25 + n + n2 = 360.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 360.25 Calculate the square root of the right side: 18.980252896 Break this problem into two subproblems by setting (n + 0.5) equal to 18.980252896 and -18.980252896.Subproblem 1
n + 0.5 = 18.980252896 Simplifying n + 0.5 = 18.980252896 Reorder the terms: 0.5 + n = 18.980252896 Solving 0.5 + n = 18.980252896 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 = 18.980252896 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 18.980252896 + -0.5 n = 18.980252896 + -0.5 Combine like terms: 18.980252896 + -0.5 = 18.480252896 n = 18.480252896 Simplifying n = 18.480252896Subproblem 2
n + 0.5 = -18.980252896 Simplifying n + 0.5 = -18.980252896 Reorder the terms: 0.5 + n = -18.980252896 Solving 0.5 + n = -18.980252896 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 = -18.980252896 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -18.980252896 + -0.5 n = -18.980252896 + -0.5 Combine like terms: -18.980252896 + -0.5 = -19.480252896 n = -19.480252896 Simplifying n = -19.480252896Solution
The solution to the problem is based on the solutions from the subproblems. n = {18.480252896, -19.480252896}
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