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Simplifying n2 + n + -525824 = 0 Reorder the terms: -525824 + n + n2 = 0 Solving -525824 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '525824' to each side of the equation. -525824 + n + 525824 + n2 = 0 + 525824 Reorder the terms: -525824 + 525824 + n + n2 = 0 + 525824 Combine like terms: -525824 + 525824 = 0 0 + n + n2 = 0 + 525824 n + n2 = 0 + 525824 Combine like terms: 0 + 525824 = 525824 n + n2 = 525824 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 = 525824 + 0.25 Reorder the terms: 0.25 + n + n2 = 525824 + 0.25 Combine like terms: 525824 + 0.25 = 525824.25 0.25 + n + n2 = 525824.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 525824.25 Calculate the square root of the right side: 725.137400773 Break this problem into two subproblems by setting (n + 0.5) equal to 725.137400773 and -725.137400773.Subproblem 1
n + 0.5 = 725.137400773 Simplifying n + 0.5 = 725.137400773 Reorder the terms: 0.5 + n = 725.137400773 Solving 0.5 + n = 725.137400773 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 = 725.137400773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 725.137400773 + -0.5 n = 725.137400773 + -0.5 Combine like terms: 725.137400773 + -0.5 = 724.637400773 n = 724.637400773 Simplifying n = 724.637400773Subproblem 2
n + 0.5 = -725.137400773 Simplifying n + 0.5 = -725.137400773 Reorder the terms: 0.5 + n = -725.137400773 Solving 0.5 + n = -725.137400773 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 = -725.137400773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -725.137400773 + -0.5 n = -725.137400773 + -0.5 Combine like terms: -725.137400773 + -0.5 = -725.637400773 n = -725.637400773 Simplifying n = -725.637400773Solution
The solution to the problem is based on the solutions from the subproblems. n = {724.637400773, -725.637400773}
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