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Simplifying -2n2 + -5n + -8 = 0 Reorder the terms: -8 + -5n + -2n2 = 0 Solving -8 + -5n + -2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 5n + 2n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 5n + 2n2)' equal to zero and attempt to solve: Simplifying 8 + 5n + 2n2 = 0 Solving 8 + 5n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 2.5n + n2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.5n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + 2.5n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.5n + n2 = 0 + -4 2.5n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.5n + n2 = -4 The n term is 2.5n. 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. 2.5n + 1.5625 + n2 = -4 + 1.5625 Reorder the terms: 1.5625 + 2.5n + n2 = -4 + 1.5625 Combine like terms: -4 + 1.5625 = -2.4375 1.5625 + 2.5n + n2 = -2.4375 Factor a perfect square on the left side: (n + 1.25)(n + 1.25) = -2.4375 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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