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Simplifying 8n4 + 6n2 = 9 Reorder the terms: 6n2 + 8n4 = 9 Solving 6n2 + 8n4 = 9 Solving for variable 'n'. Reorder the terms: -9 + 6n2 + 8n4 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 6n2 + 8n4 = 0 Factor a trinomial. (-3 + -2n2)(3 + -4n2) = 0Subproblem 1
Set the factor '(-3 + -2n2)' equal to zero and attempt to solve: Simplifying -3 + -2n2 = 0 Solving -3 + -2n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2n2 = 0 + 3 -2n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2n2 = 3 Divide each side by '-2'. n2 = -1.5 Simplifying n2 = -1.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + -4n2)' equal to zero and attempt to solve: Simplifying 3 + -4n2 = 0 Solving 3 + -4n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4n2 = 0 + -3 -4n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4n2 = -3 Divide each side by '-4'. n2 = 0.75 Simplifying n2 = 0.75 Take the square root of each side: n = {-0.866025404, 0.866025404}Solution
n = {-0.866025404, 0.866025404}
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