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Simplifying 147n4 + -84n2 + 12 = 0 Reorder the terms: 12 + -84n2 + 147n4 = 0 Solving 12 + -84n2 + 147n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -28n2 + 49n4) = 0 Factor a trinomial. 3((2 + -7n2)(2 + -7n2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -7n2)' equal to zero and attempt to solve: Simplifying 2 + -7n2 = 0 Solving 2 + -7n2 = 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 + -7n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n2 = 0 + -2 -7n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7n2 = -2 Divide each side by '-7'. n2 = 0.2857142857 Simplifying n2 = 0.2857142857 Take the square root of each side: n = {-0.534522484, 0.534522484}Subproblem 2
Set the factor '(2 + -7n2)' equal to zero and attempt to solve: Simplifying 2 + -7n2 = 0 Solving 2 + -7n2 = 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 + -7n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n2 = 0 + -2 -7n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7n2 = -2 Divide each side by '-7'. n2 = 0.2857142857 Simplifying n2 = 0.2857142857 Take the square root of each side: n = {-0.534522484, 0.534522484}Solution
n = {-0.534522484, 0.534522484, -0.534522484, 0.534522484}
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