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Simplifying n2 + n + -888 = 0 Reorder the terms: -888 + n + n2 = 0 Solving -888 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '888' to each side of the equation. -888 + n + 888 + n2 = 0 + 888 Reorder the terms: -888 + 888 + n + n2 = 0 + 888 Combine like terms: -888 + 888 = 0 0 + n + n2 = 0 + 888 n + n2 = 0 + 888 Combine like terms: 0 + 888 = 888 n + n2 = 888 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 = 888 + 0.25 Reorder the terms: 0.25 + n + n2 = 888 + 0.25 Combine like terms: 888 + 0.25 = 888.25 0.25 + n + n2 = 888.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 888.25 Calculate the square root of the right side: 29.803523282 Break this problem into two subproblems by setting (n + 0.5) equal to 29.803523282 and -29.803523282.Subproblem 1
n + 0.5 = 29.803523282 Simplifying n + 0.5 = 29.803523282 Reorder the terms: 0.5 + n = 29.803523282 Solving 0.5 + n = 29.803523282 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 = 29.803523282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 29.803523282 + -0.5 n = 29.803523282 + -0.5 Combine like terms: 29.803523282 + -0.5 = 29.303523282 n = 29.303523282 Simplifying n = 29.303523282Subproblem 2
n + 0.5 = -29.803523282 Simplifying n + 0.5 = -29.803523282 Reorder the terms: 0.5 + n = -29.803523282 Solving 0.5 + n = -29.803523282 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 = -29.803523282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -29.803523282 + -0.5 n = -29.803523282 + -0.5 Combine like terms: -29.803523282 + -0.5 = -30.303523282 n = -30.303523282 Simplifying n = -30.303523282Solution
The solution to the problem is based on the solutions from the subproblems. n = {29.303523282, -30.303523282}
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