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Simplifying n2 + n + -13 = 0 Reorder the terms: -13 + n + n2 = 0 Solving -13 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + n + 13 + n2 = 0 + 13 Reorder the terms: -13 + 13 + n + n2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + n + n2 = 0 + 13 n + n2 = 0 + 13 Combine like terms: 0 + 13 = 13 n + n2 = 13 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 = 13 + 0.25 Reorder the terms: 0.25 + n + n2 = 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + n + n2 = 13.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (n + 0.5) equal to 3.640054945 and -3.640054945.Subproblem 1
n + 0.5 = 3.640054945 Simplifying n + 0.5 = 3.640054945 Reorder the terms: 0.5 + n = 3.640054945 Solving 0.5 + n = 3.640054945 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 = 3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 3.640054945 + -0.5 n = 3.640054945 + -0.5 Combine like terms: 3.640054945 + -0.5 = 3.140054945 n = 3.140054945 Simplifying n = 3.140054945Subproblem 2
n + 0.5 = -3.640054945 Simplifying n + 0.5 = -3.640054945 Reorder the terms: 0.5 + n = -3.640054945 Solving 0.5 + n = -3.640054945 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 = -3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -3.640054945 + -0.5 n = -3.640054945 + -0.5 Combine like terms: -3.640054945 + -0.5 = -4.140054945 n = -4.140054945 Simplifying n = -4.140054945Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.140054945, -4.140054945}
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