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Simplifying n2 + -6 = 6n Reorder the terms: -6 + n2 = 6n Solving -6 + n2 = 6n Solving for variable 'n'. Reorder the terms: -6 + -6n + n2 = 6n + -6n Combine like terms: 6n + -6n = 0 -6 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -6n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + -6n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6n + n2 = 0 + 6 -6n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6n + n2 = 6 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 6 + 9 Reorder the terms: 9 + -6n + n2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + -6n + n2 = 15 Factor a perfect square on the left side: (n + -3)(n + -3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (n + -3) equal to 3.872983346 and -3.872983346.Subproblem 1
n + -3 = 3.872983346 Simplifying n + -3 = 3.872983346 Reorder the terms: -3 + n = 3.872983346 Solving -3 + n = 3.872983346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.872983346 + 3 n = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 n = 6.872983346 Simplifying n = 6.872983346Subproblem 2
n + -3 = -3.872983346 Simplifying n + -3 = -3.872983346 Reorder the terms: -3 + n = -3.872983346 Solving -3 + n = -3.872983346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.872983346 + 3 n = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 n = -0.872983346 Simplifying n = -0.872983346Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.872983346, -0.872983346}
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