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Simplifying n2 + 5n + -2 = 0 Reorder the terms: -2 + 5n + n2 = 0 Solving -2 + 5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 5n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + 5n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5n + n2 = 0 + 2 5n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 5n + n2 = 2 The n term is 5n. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5n + 6.25 + n2 = 2 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + 5n + n2 = 8.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (n + 2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
n + 2.5 = 2.872281323 Simplifying n + 2.5 = 2.872281323 Reorder the terms: 2.5 + n = 2.872281323 Solving 2.5 + n = 2.872281323 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 2.872281323 + -2.5 n = 2.872281323 + -2.5 Combine like terms: 2.872281323 + -2.5 = 0.372281323 n = 0.372281323 Simplifying n = 0.372281323Subproblem 2
n + 2.5 = -2.872281323 Simplifying n + 2.5 = -2.872281323 Reorder the terms: 2.5 + n = -2.872281323 Solving 2.5 + n = -2.872281323 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -2.872281323 + -2.5 n = -2.872281323 + -2.5 Combine like terms: -2.872281323 + -2.5 = -5.372281323 n = -5.372281323 Simplifying n = -5.372281323Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.372281323, -5.372281323}
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