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Simplifying 147n4 + -210n2 + 75 = 0 Reorder the terms: 75 + -210n2 + 147n4 = 0 Solving 75 + -210n2 + 147n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -70n2 + 49n4) = 0 Factor a trinomial. 3((5 + -7n2)(5 + -7n2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -7n2)' equal to zero and attempt to solve: Simplifying 5 + -7n2 = 0 Solving 5 + -7n2 = 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 + -7n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n2 = 0 + -5 -7n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7n2 = -5 Divide each side by '-7'. n2 = 0.7142857143 Simplifying n2 = 0.7142857143 Take the square root of each side: n = {-0.845154255, 0.845154255}Subproblem 2
Set the factor '(5 + -7n2)' equal to zero and attempt to solve: Simplifying 5 + -7n2 = 0 Solving 5 + -7n2 = 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 + -7n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n2 = 0 + -5 -7n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7n2 = -5 Divide each side by '-7'. n2 = 0.7142857143 Simplifying n2 = 0.7142857143 Take the square root of each side: n = {-0.845154255, 0.845154255}Solution
n = {-0.845154255, 0.845154255, -0.845154255, 0.845154255}
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