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Simplifying n2 + n + -1804289383 = 0 Reorder the terms: -1804289383 + n + n2 = 0 Solving -1804289383 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '1804289383' to each side of the equation. -1804289383 + n + 1804289383 + n2 = 0 + 1804289383 Reorder the terms: -1804289383 + 1804289383 + n + n2 = 0 + 1804289383 Combine like terms: -1804289383 + 1804289383 = 0 0 + n + n2 = 0 + 1804289383 n + n2 = 0 + 1804289383 Combine like terms: 0 + 1804289383 = 1804289383 n + n2 = 1804289383 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 = 1804289383 + 0.25 Reorder the terms: 0.25 + n + n2 = 1804289383 + 0.25 Combine like terms: 1804289383 + 0.25 = 1804289383.25 0.25 + n + n2 = 1804289383.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 1804289383.25 Calculate the square root of the right side: 42476.927657847 Break this problem into two subproblems by setting (n + 0.5) equal to 42476.927657847 and -42476.927657847.Subproblem 1
n + 0.5 = 42476.927657847 Simplifying n + 0.5 = 42476.927657847 Reorder the terms: 0.5 + n = 42476.927657847 Solving 0.5 + n = 42476.927657847 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 = 42476.927657847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 42476.927657847 + -0.5 n = 42476.927657847 + -0.5 Combine like terms: 42476.927657847 + -0.5 = 42476.427657847 n = 42476.427657847 Simplifying n = 42476.427657847Subproblem 2
n + 0.5 = -42476.927657847 Simplifying n + 0.5 = -42476.927657847 Reorder the terms: 0.5 + n = -42476.927657847 Solving 0.5 + n = -42476.927657847 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 = -42476.927657847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -42476.927657847 + -0.5 n = -42476.927657847 + -0.5 Combine like terms: -42476.927657847 + -0.5 = -42477.427657847 n = -42477.427657847 Simplifying n = -42477.427657847Solution
The solution to the problem is based on the solutions from the subproblems. n = {42476.427657847, -42477.427657847}
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