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Simplifying n2 + n + -3608578766 = 0 Reorder the terms: -3608578766 + n + n2 = 0 Solving -3608578766 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '3608578766' to each side of the equation. -3608578766 + n + 3608578766 + n2 = 0 + 3608578766 Reorder the terms: -3608578766 + 3608578766 + n + n2 = 0 + 3608578766 Combine like terms: -3608578766 + 3608578766 = 0 0 + n + n2 = 0 + 3608578766 n + n2 = 0 + 3608578766 Combine like terms: 0 + 3608578766 = 3608578766 n + n2 = 3608578766 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 = 3608578766 + 0.25 Reorder the terms: 0.25 + n + n2 = 3608578766 + 0.25 Combine like terms: 3608578766 + 0.25 = 3608578766.25 0.25 + n + n2 = 3608578766.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 3608578766.25 Calculate the square root of the right side: 60071.447179588 Break this problem into two subproblems by setting (n + 0.5) equal to 60071.447179588 and -60071.447179588.Subproblem 1
n + 0.5 = 60071.447179588 Simplifying n + 0.5 = 60071.447179588 Reorder the terms: 0.5 + n = 60071.447179588 Solving 0.5 + n = 60071.447179588 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 = 60071.447179588 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 60071.447179588 + -0.5 n = 60071.447179588 + -0.5 Combine like terms: 60071.447179588 + -0.5 = 60070.947179588 n = 60070.947179588 Simplifying n = 60070.947179588Subproblem 2
n + 0.5 = -60071.447179588 Simplifying n + 0.5 = -60071.447179588 Reorder the terms: 0.5 + n = -60071.447179588 Solving 0.5 + n = -60071.447179588 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 = -60071.447179588 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -60071.447179588 + -0.5 n = -60071.447179588 + -0.5 Combine like terms: -60071.447179588 + -0.5 = -60071.947179588 n = -60071.947179588 Simplifying n = -60071.947179588Solution
The solution to the problem is based on the solutions from the subproblems. n = {60070.947179588, -60071.947179588}
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