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Simplifying n2 + 2n + -4 = 88 Reorder the terms: -4 + 2n + n2 = 88 Solving -4 + 2n + n2 = 88 Solving for variable 'n'. Reorder the terms: -4 + -88 + 2n + n2 = 88 + -88 Combine like terms: -4 + -88 = -92 -92 + 2n + n2 = 88 + -88 Combine like terms: 88 + -88 = 0 -92 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 2n + 92 + n2 = 0 + 92 Reorder the terms: -92 + 92 + 2n + n2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 2n + n2 = 0 + 92 2n + n2 = 0 + 92 Combine like terms: 0 + 92 = 92 2n + n2 = 92 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 92 + 1 Reorder the terms: 1 + 2n + n2 = 92 + 1 Combine like terms: 92 + 1 = 93 1 + 2n + n2 = 93 Factor a perfect square on the left side: (n + 1)(n + 1) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (n + 1) equal to 9.643650761 and -9.643650761.Subproblem 1
n + 1 = 9.643650761 Simplifying n + 1 = 9.643650761 Reorder the terms: 1 + n = 9.643650761 Solving 1 + n = 9.643650761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 9.643650761 + -1 Combine like terms: 1 + -1 = 0 0 + n = 9.643650761 + -1 n = 9.643650761 + -1 Combine like terms: 9.643650761 + -1 = 8.643650761 n = 8.643650761 Simplifying n = 8.643650761Subproblem 2
n + 1 = -9.643650761 Simplifying n + 1 = -9.643650761 Reorder the terms: 1 + n = -9.643650761 Solving 1 + n = -9.643650761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -9.643650761 + -1 Combine like terms: 1 + -1 = 0 0 + n = -9.643650761 + -1 n = -9.643650761 + -1 Combine like terms: -9.643650761 + -1 = -10.643650761 n = -10.643650761 Simplifying n = -10.643650761Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.643650761, -10.643650761}
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