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Simplifying 4n4 + 3n2 + -1 = 0 Reorder the terms: -1 + 3n2 + 4n4 = 0 Solving -1 + 3n2 + 4n4 = 0 Solving for variable 'n'. Factor a trinomial. (-1 + -1n2)(1 + -4n2) = 0 Factor a difference between two squares. (-1 + -1n2)((1 + 2n)(1 + -2n)) = 0Subproblem 1
Set the factor '(-1 + -1n2)' equal to zero and attempt to solve: Simplifying -1 + -1n2 = 0 Solving -1 + -1n2 = 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 + -1n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n2 = 0 + 1 -1n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1n2 = 1 Divide each side by '-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 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 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 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Subproblem 3
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-0.5, 0.5}
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