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Simplifying (2n4 + -10n2) + -1(4n4 + -5n2 + 5) = 0 Reorder the terms: (-10n2 + 2n4) + -1(4n4 + -5n2 + 5) = 0 Remove parenthesis around (-10n2 + 2n4) -10n2 + 2n4 + -1(4n4 + -5n2 + 5) = 0 Reorder the terms: -10n2 + 2n4 + -1(5 + -5n2 + 4n4) = 0 -10n2 + 2n4 + (5 * -1 + -5n2 * -1 + 4n4 * -1) = 0 -10n2 + 2n4 + (-5 + 5n2 + -4n4) = 0 Reorder the terms: -5 + -10n2 + 5n2 + 2n4 + -4n4 = 0 Combine like terms: -10n2 + 5n2 = -5n2 -5 + -5n2 + 2n4 + -4n4 = 0 Combine like terms: 2n4 + -4n4 = -2n4 -5 + -5n2 + -2n4 = 0 Solving -5 + -5n2 + -2n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 5n2 + 2n4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 5n2 + 2n4)' equal to zero and attempt to solve: Simplifying 5 + 5n2 + 2n4 = 0 Solving 5 + 5n2 + 2n4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 2.5n2 + n4 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 2.5n2 + -2.5 + n4 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 2.5n2 + n4 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 2.5n2 + n4 = 0 + -2.5 2.5n2 + n4 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 2.5n2 + n4 = -2.5 The n term is 2.5n2. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5n2 + 1.5625 + n4 = -2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5n2 + n4 = -2.5 + 1.5625 Combine like terms: -2.5 + 1.5625 = -0.9375 1.5625 + 2.5n2 + n4 = -0.9375 Factor a perfect square on the left side: (n2 + 1.25)(n2 + 1.25) = -0.9375 Can't calculate square root of the right side. 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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