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Simplifying n2 + -4n = 11 Reorder the terms: -4n + n2 = 11 Solving -4n + n2 = 11 Solving for variable 'n'. Reorder the terms: -11 + -4n + n2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -4n + 11 + n2 = 0 + 11 Reorder the terms: -11 + 11 + -4n + n2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4n + n2 = 0 + 11 -4n + n2 = 0 + 11 Combine like terms: 0 + 11 = 11 -4n + n2 = 11 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 11 + 4 Reorder the terms: 4 + -4n + n2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + -4n + n2 = 15 Factor a perfect square on the left side: (n + -2)(n + -2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (n + -2) equal to 3.872983346 and -3.872983346.Subproblem 1
n + -2 = 3.872983346 Simplifying n + -2 = 3.872983346 Reorder the terms: -2 + n = 3.872983346 Solving -2 + n = 3.872983346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + n = 3.872983346 + 2 n = 3.872983346 + 2 Combine like terms: 3.872983346 + 2 = 5.872983346 n = 5.872983346 Simplifying n = 5.872983346Subproblem 2
n + -2 = -3.872983346 Simplifying n + -2 = -3.872983346 Reorder the terms: -2 + n = -3.872983346 Solving -2 + n = -3.872983346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + n = -3.872983346 + 2 n = -3.872983346 + 2 Combine like terms: -3.872983346 + 2 = -1.872983346 n = -1.872983346 Simplifying n = -1.872983346Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.872983346, -1.872983346}
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