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Simplifying n2 + -1n + -1 = 104 Reorder the terms: -1 + -1n + n2 = 104 Solving -1 + -1n + n2 = 104 Solving for variable 'n'. Reorder the terms: -1 + -104 + -1n + n2 = 104 + -104 Combine like terms: -1 + -104 = -105 -105 + -1n + n2 = 104 + -104 Combine like terms: 104 + -104 = 0 -105 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + -1n + 105 + n2 = 0 + 105 Reorder the terms: -105 + 105 + -1n + n2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + -1n + n2 = 0 + 105 -1n + n2 = 0 + 105 Combine like terms: 0 + 105 = 105 -1n + n2 = 105 The n term is -1n. 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. -1n + 0.25 + n2 = 105 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 105 + 0.25 Combine like terms: 105 + 0.25 = 105.25 0.25 + -1n + n2 = 105.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 105.25 Calculate the square root of the right side: 10.259142264 Break this problem into two subproblems by setting (n + -0.5) equal to 10.259142264 and -10.259142264.Subproblem 1
n + -0.5 = 10.259142264 Simplifying n + -0.5 = 10.259142264 Reorder the terms: -0.5 + n = 10.259142264 Solving -0.5 + n = 10.259142264 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 = 10.259142264 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 10.259142264 + 0.5 n = 10.259142264 + 0.5 Combine like terms: 10.259142264 + 0.5 = 10.759142264 n = 10.759142264 Simplifying n = 10.759142264Subproblem 2
n + -0.5 = -10.259142264 Simplifying n + -0.5 = -10.259142264 Reorder the terms: -0.5 + n = -10.259142264 Solving -0.5 + n = -10.259142264 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 = -10.259142264 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -10.259142264 + 0.5 n = -10.259142264 + 0.5 Combine like terms: -10.259142264 + 0.5 = -9.759142264 n = -9.759142264 Simplifying n = -9.759142264Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.759142264, -9.759142264}
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