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Simplifying 30n4 + 15n2 + 1 = 0 Reorder the terms: 1 + 15n2 + 30n4 = 0 Solving 1 + 15n2 + 30n4 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.03333333333 + 0.5n2 + n4 = 0 Move the constant term to the right: Add '-0.03333333333' to each side of the equation. 0.03333333333 + 0.5n2 + -0.03333333333 + n4 = 0 + -0.03333333333 Reorder the terms: 0.03333333333 + -0.03333333333 + 0.5n2 + n4 = 0 + -0.03333333333 Combine like terms: 0.03333333333 + -0.03333333333 = 0.00000000000 0.00000000000 + 0.5n2 + n4 = 0 + -0.03333333333 0.5n2 + n4 = 0 + -0.03333333333 Combine like terms: 0 + -0.03333333333 = -0.03333333333 0.5n2 + n4 = -0.03333333333 The n term is 0.5n2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5n2 + 0.0625 + n4 = -0.03333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5n2 + n4 = -0.03333333333 + 0.0625 Combine like terms: -0.03333333333 + 0.0625 = 0.02916666667 0.0625 + 0.5n2 + n4 = 0.02916666667 Factor a perfect square on the left side: (n2 + 0.25)(n2 + 0.25) = 0.02916666667 Calculate the square root of the right side: 0.170782513 Break this problem into two subproblems by setting (n2 + 0.25) equal to 0.170782513 and -0.170782513.Subproblem 1
n2 + 0.25 = 0.170782513 Simplifying n2 + 0.25 = 0.170782513 Reorder the terms: 0.25 + n2 = 0.170782513 Solving 0.25 + n2 = 0.170782513 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + n2 = 0.170782513 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + n2 = 0.170782513 + -0.25 n2 = 0.170782513 + -0.25 Combine like terms: 0.170782513 + -0.25 = -0.079217487 n2 = -0.079217487 Simplifying n2 = -0.079217487 Reorder the terms: 0.079217487 + n2 = -0.079217487 + 0.079217487 Combine like terms: -0.079217487 + 0.079217487 = 0.000000000 0.079217487 + n2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
n2 + 0.25 = -0.170782513 Simplifying n2 + 0.25 = -0.170782513 Reorder the terms: 0.25 + n2 = -0.170782513 Solving 0.25 + n2 = -0.170782513 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + n2 = -0.170782513 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + n2 = -0.170782513 + -0.25 n2 = -0.170782513 + -0.25 Combine like terms: -0.170782513 + -0.25 = -0.420782513 n2 = -0.420782513 Simplifying n2 = -0.420782513 Reorder the terms: 0.420782513 + n2 = -0.420782513 + 0.420782513 Combine like terms: -0.420782513 + 0.420782513 = 0.000000000 0.420782513 + n2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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