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Simplifying 3n4 + -33n2 + 72 = 0 Reorder the terms: 72 + -33n2 + 3n4 = 0 Solving 72 + -33n2 + 3n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(24 + -11n2 + n4) = 0 Factor a trinomial. 3((3 + -1n2)(8 + -1n2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1n2)' equal to zero and attempt to solve: Simplifying 3 + -1n2 = 0 Solving 3 + -1n2 = 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 + -1n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n2 = 0 + -3 -1n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1n2 = -3 Divide each side by '-1'. n2 = 3 Simplifying n2 = 3 Take the square root of each side: n = {-1.732050808, 1.732050808}Subproblem 2
Set the factor '(8 + -1n2)' equal to zero and attempt to solve: Simplifying 8 + -1n2 = 0 Solving 8 + -1n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n2 = 0 + -8 -1n2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1n2 = -8 Divide each side by '-1'. n2 = 8 Simplifying n2 = 8 Take the square root of each side: n = {-2.828427125, 2.828427125}Solution
n = {-1.732050808, 1.732050808, -2.828427125, 2.828427125}
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