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Simplifying 100 + -120n2 + 36n4 = 0 Solving 100 + -120n2 + 36n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -30n2 + 9n4) = 0 Factor a trinomial. 4((5 + -3n2)(5 + -3n2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -3n2)' equal to zero and attempt to solve: Simplifying 5 + -3n2 = 0 Solving 5 + -3n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n2 = 0 + -5 -3n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3n2 = -5 Divide each side by '-3'. n2 = 1.666666667 Simplifying n2 = 1.666666667 Take the square root of each side: n = {-1.290994449, 1.290994449}Subproblem 2
Set the factor '(5 + -3n2)' equal to zero and attempt to solve: Simplifying 5 + -3n2 = 0 Solving 5 + -3n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n2 = 0 + -5 -3n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3n2 = -5 Divide each side by '-3'. n2 = 1.666666667 Simplifying n2 = 1.666666667 Take the square root of each side: n = {-1.290994449, 1.290994449}Solution
n = {-1.290994449, 1.290994449, -1.290994449, 1.290994449}
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