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Simplifying 18n2 + 2n + 6 = 0 Reorder the terms: 6 + 2n + 18n2 = 0 Solving 6 + 2n + 18n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + n + 9n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + n + 9n2)' equal to zero and attempt to solve: Simplifying 3 + n + 9n2 = 0 Solving 3 + n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + 0.1111111111n + n2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.1111111111n + -0.3333333333 + n2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.1111111111n + n2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.1111111111n + n2 = 0 + -0.3333333333 0.1111111111n + n2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.1111111111n + n2 = -0.3333333333 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. 0.1111111111n + 0.25 + n2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + 0.1111111111n + n2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + 0.1111111111n + n2 = -0.0833333333 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -0.0833333333 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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