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Simplifying 6n2 + 2n = -104 Reorder the terms: 2n + 6n2 = -104 Solving 2n + 6n2 = -104 Solving for variable 'n'. Reorder the terms: 104 + 2n + 6n2 = -104 + 104 Combine like terms: -104 + 104 = 0 104 + 2n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(52 + n + 3n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(52 + n + 3n2)' equal to zero and attempt to solve: Simplifying 52 + n + 3n2 = 0 Solving 52 + n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 17.33333333 + 0.3333333333n + n2 = 0 Move the constant term to the right: Add '-17.33333333' to each side of the equation. 17.33333333 + 0.3333333333n + -17.33333333 + n2 = 0 + -17.33333333 Reorder the terms: 17.33333333 + -17.33333333 + 0.3333333333n + n2 = 0 + -17.33333333 Combine like terms: 17.33333333 + -17.33333333 = 0.00000000 0.00000000 + 0.3333333333n + n2 = 0 + -17.33333333 0.3333333333n + n2 = 0 + -17.33333333 Combine like terms: 0 + -17.33333333 = -17.33333333 0.3333333333n + n2 = -17.33333333 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333n + 0.25 + n2 = -17.33333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333n + n2 = -17.33333333 + 0.25 Combine like terms: -17.33333333 + 0.25 = -17.08333333 0.25 + 0.3333333333n + n2 = -17.08333333 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -17.08333333 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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