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Simplifying n2 + -1n + -30 = 30 Reorder the terms: -30 + -1n + n2 = 30 Solving -30 + -1n + n2 = 30 Solving for variable 'n'. Reorder the terms: -30 + -30 + -1n + n2 = 30 + -30 Combine like terms: -30 + -30 = -60 -60 + -1n + n2 = 30 + -30 Combine like terms: 30 + -30 = 0 -60 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -1n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + -1n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -1n + n2 = 0 + 60 -1n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 -1n + n2 = 60 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 = 60 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 60 + 0.25 Combine like terms: 60 + 0.25 = 60.25 0.25 + -1n + n2 = 60.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (n + -0.5) equal to 7.762087348 and -7.762087348.Subproblem 1
n + -0.5 = 7.762087348 Simplifying n + -0.5 = 7.762087348 Reorder the terms: -0.5 + n = 7.762087348 Solving -0.5 + n = 7.762087348 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 = 7.762087348 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 7.762087348 + 0.5 n = 7.762087348 + 0.5 Combine like terms: 7.762087348 + 0.5 = 8.262087348 n = 8.262087348 Simplifying n = 8.262087348Subproblem 2
n + -0.5 = -7.762087348 Simplifying n + -0.5 = -7.762087348 Reorder the terms: -0.5 + n = -7.762087348 Solving -0.5 + n = -7.762087348 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 = -7.762087348 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -7.762087348 + 0.5 n = -7.762087348 + 0.5 Combine like terms: -7.762087348 + 0.5 = -7.262087348 n = -7.262087348 Simplifying n = -7.262087348Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.262087348, -7.262087348}
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