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Simplifying n2 + n + -600000000 = 0 Reorder the terms: -600000000 + n + n2 = 0 Solving -600000000 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '600000000' to each side of the equation. -600000000 + n + 600000000 + n2 = 0 + 600000000 Reorder the terms: -600000000 + 600000000 + n + n2 = 0 + 600000000 Combine like terms: -600000000 + 600000000 = 0 0 + n + n2 = 0 + 600000000 n + n2 = 0 + 600000000 Combine like terms: 0 + 600000000 = 600000000 n + n2 = 600000000 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 = 600000000 + 0.25 Reorder the terms: 0.25 + n + n2 = 600000000 + 0.25 Combine like terms: 600000000 + 0.25 = 600000000.25 0.25 + n + n2 = 600000000.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 600000000.25 Calculate the square root of the right side: 24494.897432935 Break this problem into two subproblems by setting (n + 0.5) equal to 24494.897432935 and -24494.897432935.Subproblem 1
n + 0.5 = 24494.897432935 Simplifying n + 0.5 = 24494.897432935 Reorder the terms: 0.5 + n = 24494.897432935 Solving 0.5 + n = 24494.897432935 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 = 24494.897432935 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 24494.897432935 + -0.5 n = 24494.897432935 + -0.5 Combine like terms: 24494.897432935 + -0.5 = 24494.397432935 n = 24494.397432935 Simplifying n = 24494.397432935Subproblem 2
n + 0.5 = -24494.897432935 Simplifying n + 0.5 = -24494.897432935 Reorder the terms: 0.5 + n = -24494.897432935 Solving 0.5 + n = -24494.897432935 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 = -24494.897432935 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -24494.897432935 + -0.5 n = -24494.897432935 + -0.5 Combine like terms: -24494.897432935 + -0.5 = -24495.397432935 n = -24495.397432935 Simplifying n = -24495.397432935Solution
The solution to the problem is based on the solutions from the subproblems. n = {24494.397432935, -24495.397432935}
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