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Simplifying 9n4 + -37n2 + 4 = 0 Reorder the terms: 4 + -37n2 + 9n4 = 0 Solving 4 + -37n2 + 9n4 = 0 Solving for variable 'n'. Factor a trinomial. (1 + -9n2)(4 + -1n2) = 0 Factor a difference between two squares. ((1 + 3n)(1 + -3n))(4 + -1n2) = 0 Factor a difference between two squares. ((2 + n)(2 + -1n))(1 + 3n)(1 + -3n) = 0Subproblem 1
Set the factor '(1 + 3n)' equal to zero and attempt to solve: Simplifying 1 + 3n = 0 Solving 1 + 3n = 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 + 3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3n = 0 + -1 3n = 0 + -1 Combine like terms: 0 + -1 = -1 3n = -1 Divide each side by '3'. n = -0.3333333333 Simplifying n = -0.3333333333Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 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 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Subproblem 3
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 4
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {-0.3333333333, 0.3333333333, -2, 2}
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