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Simplifying n2 + n + -14.9769 = 0 Reorder the terms: -14.9769 + n + n2 = 0 Solving -14.9769 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '14.9769' to each side of the equation. -14.9769 + n + 14.9769 + n2 = 0 + 14.9769 Reorder the terms: -14.9769 + 14.9769 + n + n2 = 0 + 14.9769 Combine like terms: -14.9769 + 14.9769 = 0.0000 0.0000 + n + n2 = 0 + 14.9769 n + n2 = 0 + 14.9769 Combine like terms: 0 + 14.9769 = 14.9769 n + n2 = 14.9769 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 = 14.9769 + 0.25 Reorder the terms: 0.25 + n + n2 = 14.9769 + 0.25 Combine like terms: 14.9769 + 0.25 = 15.2269 0.25 + n + n2 = 15.2269 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 15.2269 Calculate the square root of the right side: 3.902166065 Break this problem into two subproblems by setting (n + 0.5) equal to 3.902166065 and -3.902166065.Subproblem 1
n + 0.5 = 3.902166065 Simplifying n + 0.5 = 3.902166065 Reorder the terms: 0.5 + n = 3.902166065 Solving 0.5 + n = 3.902166065 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 = 3.902166065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 3.902166065 + -0.5 n = 3.902166065 + -0.5 Combine like terms: 3.902166065 + -0.5 = 3.402166065 n = 3.402166065 Simplifying n = 3.402166065Subproblem 2
n + 0.5 = -3.902166065 Simplifying n + 0.5 = -3.902166065 Reorder the terms: 0.5 + n = -3.902166065 Solving 0.5 + n = -3.902166065 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 = -3.902166065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -3.902166065 + -0.5 n = -3.902166065 + -0.5 Combine like terms: -3.902166065 + -0.5 = -4.402166065 n = -4.402166065 Simplifying n = -4.402166065Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.402166065, -4.402166065}
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