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Simplifying 32n4 + -112n2 + 98 = 0 Reorder the terms: 98 + -112n2 + 32n4 = 0 Solving 98 + -112n2 + 32n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -56n2 + 16n4) = 0 Factor a trinomial. 2((7 + -4n2)(7 + -4n2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -4n2)' equal to zero and attempt to solve: Simplifying 7 + -4n2 = 0 Solving 7 + -4n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4n2 = 0 + -7 -4n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -4n2 = -7 Divide each side by '-4'. n2 = 1.75 Simplifying n2 = 1.75 Take the square root of each side: n = {-1.322875656, 1.322875656}Subproblem 2
Set the factor '(7 + -4n2)' equal to zero and attempt to solve: Simplifying 7 + -4n2 = 0 Solving 7 + -4n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4n2 = 0 + -7 -4n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -4n2 = -7 Divide each side by '-4'. n2 = 1.75 Simplifying n2 = 1.75 Take the square root of each side: n = {-1.322875656, 1.322875656}Solution
n = {-1.322875656, 1.322875656, -1.322875656, 1.322875656}
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