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Simplifying n2 + -2n = 11 Reorder the terms: -2n + n2 = 11 Solving -2n + n2 = 11 Solving for variable 'n'. Reorder the terms: -11 + -2n + n2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -2n + 11 + n2 = 0 + 11 Reorder the terms: -11 + 11 + -2n + n2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2n + n2 = 0 + 11 -2n + n2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2n + n2 = 11 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 = 11 + 1 Reorder the terms: 1 + -2n + n2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + -2n + n2 = 12 Factor a perfect square on the left side: (n + -1)(n + -1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (n + -1) equal to 3.464101615 and -3.464101615.Subproblem 1
n + -1 = 3.464101615 Simplifying n + -1 = 3.464101615 Reorder the terms: -1 + n = 3.464101615 Solving -1 + n = 3.464101615 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 = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + n = 3.464101615 + 1 n = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 n = 4.464101615 Simplifying n = 4.464101615Subproblem 2
n + -1 = -3.464101615 Simplifying n + -1 = -3.464101615 Reorder the terms: -1 + n = -3.464101615 Solving -1 + n = -3.464101615 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 = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + n = -3.464101615 + 1 n = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 n = -2.464101615 Simplifying n = -2.464101615Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.464101615, -2.464101615}
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