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Simplifying 0 = 30n2 + 18n + 54 Reorder the terms: 0 = 54 + 18n + 30n2 Solving 0 = 54 + 18n + 30n2 Solving for variable 'n'. Combine like terms: 0 + -54 = -54 -54 + -18n + -30n2 = 54 + 18n + 30n2 + -54 + -18n + -30n2 Reorder the terms: -54 + -18n + -30n2 = 54 + -54 + 18n + -18n + 30n2 + -30n2 Combine like terms: 54 + -54 = 0 -54 + -18n + -30n2 = 0 + 18n + -18n + 30n2 + -30n2 -54 + -18n + -30n2 = 18n + -18n + 30n2 + -30n2 Combine like terms: 18n + -18n = 0 -54 + -18n + -30n2 = 0 + 30n2 + -30n2 -54 + -18n + -30n2 = 30n2 + -30n2 Combine like terms: 30n2 + -30n2 = 0 -54 + -18n + -30n2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(9 + 3n + 5n2) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(9 + 3n + 5n2)' equal to zero and attempt to solve: Simplifying 9 + 3n + 5n2 = 0 Solving 9 + 3n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 0.6n + n2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 0.6n + -1.8 + n2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 0.6n + n2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 0.6n + n2 = 0 + -1.8 0.6n + n2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 0.6n + n2 = -1.8 The n term is 0.6n. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6n + 0.09 + n2 = -1.8 + 0.09 Reorder the terms: 0.09 + 0.6n + n2 = -1.8 + 0.09 Combine like terms: -1.8 + 0.09 = -1.71 0.09 + 0.6n + n2 = -1.71 Factor a perfect square on the left side: (n + 0.3)(n + 0.3) = -1.71 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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