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Simplifying 6n2 + 3n + 9 = 0 Reorder the terms: 9 + 3n + 6n2 = 0 Solving 9 + 3n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + n + 2n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + n + 2n2)' equal to zero and attempt to solve: Simplifying 3 + n + 2n2 = 0 Solving 3 + n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 0.5n + n2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 0.5n + -1.5 + n2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 0.5n + n2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 0.5n + n2 = 0 + -1.5 0.5n + n2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 0.5n + n2 = -1.5 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. 0.5n + 0.25 + n2 = -1.5 + 0.25 Reorder the terms: 0.25 + 0.5n + n2 = -1.5 + 0.25 Combine like terms: -1.5 + 0.25 = -1.25 0.25 + 0.5n + n2 = -1.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -1.25 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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