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Simplifying 11n8 + 4n4 = 15 Reorder the terms: 4n4 + 11n8 = 15 Solving 4n4 + 11n8 = 15 Solving for variable 'n'. Reorder the terms: -15 + 4n4 + 11n8 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 4n4 + 11n8 = 0 Factor a trinomial. (-15 + -11n4)(1 + -1n4) = 0 Factor a difference between two squares. (-15 + -11n4)((1 + n2)(1 + -1n2)) = 0 Factor a difference between two squares. (-15 + -11n4)((1 + n2)((1 + n)(1 + -1n))) = 0Subproblem 1
Set the factor '(-15 + -11n4)' equal to zero and attempt to solve: Simplifying -15 + -11n4 = 0 Solving -15 + -11n4 = 0 Move all terms containing n to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -11n4 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -11n4 = 0 + 15 -11n4 = 0 + 15 Combine like terms: 0 + 15 = 15 -11n4 = 15 Divide each side by '-11'. n4 = -1.363636364 Simplifying n4 = -1.363636364 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 '(1 + n2)' equal to zero and attempt to solve: Simplifying 1 + n2 = 0 Solving 1 + n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n2 = 0 + -1 n2 = 0 + -1 Combine like terms: 0 + -1 = -1 n2 = -1 Simplifying n2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 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 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Subproblem 4
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-1, 1}
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