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Simplifying -6n2 + 6n + -5 = -4n2 + 10n Reorder the terms: -5 + 6n + -6n2 = -4n2 + 10n Reorder the terms: -5 + 6n + -6n2 = 10n + -4n2 Solving -5 + 6n + -6n2 = 10n + -4n2 Solving for variable 'n'. Reorder the terms: -5 + 6n + -10n + -6n2 + 4n2 = 10n + -4n2 + -10n + 4n2 Combine like terms: 6n + -10n = -4n -5 + -4n + -6n2 + 4n2 = 10n + -4n2 + -10n + 4n2 Combine like terms: -6n2 + 4n2 = -2n2 -5 + -4n + -2n2 = 10n + -4n2 + -10n + 4n2 Reorder the terms: -5 + -4n + -2n2 = 10n + -10n + -4n2 + 4n2 Combine like terms: 10n + -10n = 0 -5 + -4n + -2n2 = 0 + -4n2 + 4n2 -5 + -4n + -2n2 = -4n2 + 4n2 Combine like terms: -4n2 + 4n2 = 0 -5 + -4n + -2n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 4n + 2n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 4n + 2n2)' equal to zero and attempt to solve: Simplifying 5 + 4n + 2n2 = 0 Solving 5 + 4n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 2n + n2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 2n + -2.5 + n2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 2n + n2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 2n + n2 = 0 + -2.5 2n + n2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 2n + n2 = -2.5 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = -2.5 + 1 Reorder the terms: 1 + 2n + n2 = -2.5 + 1 Combine like terms: -2.5 + 1 = -1.5 1 + 2n + n2 = -1.5 Factor a perfect square on the left side: (n + 1)(n + 1) = -1.5 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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