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Simplifying 8n2 = -26n + -48 Reorder the terms: 8n2 = -48 + -26n Solving 8n2 = -48 + -26n Solving for variable 'n'. Reorder the terms: 48 + 26n + 8n2 = -48 + -26n + 48 + 26n Reorder the terms: 48 + 26n + 8n2 = -48 + 48 + -26n + 26n Combine like terms: -48 + 48 = 0 48 + 26n + 8n2 = 0 + -26n + 26n 48 + 26n + 8n2 = -26n + 26n Combine like terms: -26n + 26n = 0 48 + 26n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 13n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + 13n + 4n2)' equal to zero and attempt to solve: Simplifying 24 + 13n + 4n2 = 0 Solving 24 + 13n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6 + 3.25n + n2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 3.25n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + 3.25n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 3.25n + n2 = 0 + -6 3.25n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 3.25n + n2 = -6 The n term is 3.25n. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25n + 2.640625 + n2 = -6 + 2.640625 Reorder the terms: 2.640625 + 3.25n + n2 = -6 + 2.640625 Combine like terms: -6 + 2.640625 = -3.359375 2.640625 + 3.25n + n2 = -3.359375 Factor a perfect square on the left side: (n + 1.625)(n + 1.625) = -3.359375 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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