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Simplifying n4 + -6n2 + -9 = 0 Reorder the terms: -9 + -6n2 + n4 = 0 Solving -9 + -6n2 + n4 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6n2 + 9 + n4 = 0 + 9 Reorder the terms: -9 + 9 + -6n2 + n4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6n2 + n4 = 0 + 9 -6n2 + n4 = 0 + 9 Combine like terms: 0 + 9 = 9 -6n2 + n4 = 9 The n term is -6n2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n2 + 9 + n4 = 9 + 9 Reorder the terms: 9 + -6n2 + n4 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6n2 + n4 = 18 Factor a perfect square on the left side: (n2 + -3)(n2 + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (n2 + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
n2 + -3 = 4.242640687 Simplifying n2 + -3 = 4.242640687 Reorder the terms: -3 + n2 = 4.242640687 Solving -3 + n2 = 4.242640687 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 + n2 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + n2 = 4.242640687 + 3 n2 = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 n2 = 7.242640687 Simplifying n2 = 7.242640687 Take the square root of each side: n = {-2.691215466, 2.691215466}Subproblem 2
n2 + -3 = -4.242640687 Simplifying n2 + -3 = -4.242640687 Reorder the terms: -3 + n2 = -4.242640687 Solving -3 + n2 = -4.242640687 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 + n2 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + n2 = -4.242640687 + 3 n2 = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 n2 = -1.242640687 Simplifying n2 = -1.242640687 Reorder the terms: 1.242640687 + n2 = -1.242640687 + 1.242640687 Combine like terms: -1.242640687 + 1.242640687 = 0.000000000 1.242640687 + n2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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