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Simplifying -2n(4n + 5) = -6(n + -3) + -8 Reorder the terms: -2n(5 + 4n) = -6(n + -3) + -8 (5 * -2n + 4n * -2n) = -6(n + -3) + -8 (-10n + -8n2) = -6(n + -3) + -8 Reorder the terms: -10n + -8n2 = -6(-3 + n) + -8 -10n + -8n2 = (-3 * -6 + n * -6) + -8 -10n + -8n2 = (18 + -6n) + -8 Reorder the terms: -10n + -8n2 = 18 + -8 + -6n Combine like terms: 18 + -8 = 10 -10n + -8n2 = 10 + -6n Solving -10n + -8n2 = 10 + -6n Solving for variable 'n'. Reorder the terms: -10 + -10n + 6n + -8n2 = 10 + -6n + -10 + 6n Combine like terms: -10n + 6n = -4n -10 + -4n + -8n2 = 10 + -6n + -10 + 6n Reorder the terms: -10 + -4n + -8n2 = 10 + -10 + -6n + 6n Combine like terms: 10 + -10 = 0 -10 + -4n + -8n2 = 0 + -6n + 6n -10 + -4n + -8n2 = -6n + 6n Combine like terms: -6n + 6n = 0 -10 + -4n + -8n2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 2n + 4n2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 2n + 4n2)' equal to zero and attempt to solve: Simplifying 5 + 2n + 4n2 = 0 Solving 5 + 2n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.5n + n2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.5n + -1.25 + n2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.5n + n2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.5n + n2 = 0 + -1.25 0.5n + n2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.5n + n2 = -1.25 The n term is 0.5n. 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. 0.5n + 0.0625 + n2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + 0.5n + n2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + 0.5n + n2 = -1.1875 Factor a perfect square on the left side: (n + 0.25)(n + 0.25) = -1.1875 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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