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Simplifying 50n4 + -40n2 + 8 = 0 Reorder the terms: 8 + -40n2 + 50n4 = 0 Solving 8 + -40n2 + 50n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -20n2 + 25n4) = 0 Factor a trinomial. 2((2 + -5n2)(2 + -5n2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -5n2)' equal to zero and attempt to solve: Simplifying 2 + -5n2 = 0 Solving 2 + -5n2 = 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 + -5n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n2 = 0 + -2 -5n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5n2 = -2 Divide each side by '-5'. n2 = 0.4 Simplifying n2 = 0.4 Take the square root of each side: n = {-0.632455532, 0.632455532}Subproblem 2
Set the factor '(2 + -5n2)' equal to zero and attempt to solve: Simplifying 2 + -5n2 = 0 Solving 2 + -5n2 = 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 + -5n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n2 = 0 + -2 -5n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5n2 = -2 Divide each side by '-5'. n2 = 0.4 Simplifying n2 = 0.4 Take the square root of each side: n = {-0.632455532, 0.632455532}Solution
n = {-0.632455532, 0.632455532, -0.632455532, 0.632455532}
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