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Simplifying (n)(n) + n = 88 Multiply n * n n2 + n = 88 Reorder the terms: n + n2 = 88 Solving n + n2 = 88 Solving for variable 'n'. Reorder the terms: -88 + n + n2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + n + 88 + n2 = 0 + 88 Reorder the terms: -88 + 88 + n + n2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + n + n2 = 0 + 88 n + n2 = 0 + 88 Combine like terms: 0 + 88 = 88 n + n2 = 88 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 = 88 + 0.25 Reorder the terms: 0.25 + n + n2 = 88 + 0.25 Combine like terms: 88 + 0.25 = 88.25 0.25 + n + n2 = 88.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (n + 0.5) equal to 9.394147114 and -9.394147114.Subproblem 1
n + 0.5 = 9.394147114 Simplifying n + 0.5 = 9.394147114 Reorder the terms: 0.5 + n = 9.394147114 Solving 0.5 + n = 9.394147114 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 = 9.394147114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 9.394147114 + -0.5 n = 9.394147114 + -0.5 Combine like terms: 9.394147114 + -0.5 = 8.894147114 n = 8.894147114 Simplifying n = 8.894147114Subproblem 2
n + 0.5 = -9.394147114 Simplifying n + 0.5 = -9.394147114 Reorder the terms: 0.5 + n = -9.394147114 Solving 0.5 + n = -9.394147114 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 = -9.394147114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -9.394147114 + -0.5 n = -9.394147114 + -0.5 Combine like terms: -9.394147114 + -0.5 = -9.894147114 n = -9.894147114 Simplifying n = -9.894147114Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.894147114, -9.894147114}
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