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Simplifying 8(10n + 15) + 18n(1 + 16n) = 0 Reorder the terms: 8(15 + 10n) + 18n(1 + 16n) = 0 (15 * 8 + 10n * 8) + 18n(1 + 16n) = 0 (120 + 80n) + 18n(1 + 16n) = 0 120 + 80n + (1 * 18n + 16n * 18n) = 0 120 + 80n + (18n + 288n2) = 0 Combine like terms: 80n + 18n = 98n 120 + 98n + 288n2 = 0 Solving 120 + 98n + 288n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(60 + 49n + 144n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + 49n + 144n2)' equal to zero and attempt to solve: Simplifying 60 + 49n + 144n2 = 0 Solving 60 + 49n + 144n2 = 0 Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. 0.4166666667 + 0.3402777778n + n2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 0.3402777778n + -0.4166666667 + n2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 0.3402777778n + n2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 0.3402777778n + n2 = 0 + -0.4166666667 0.3402777778n + n2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 0.3402777778n + n2 = -0.4166666667 The n term is 0.3402777778n. Take half its coefficient (0.1701388889). Square it (0.02894724152) and add it to both sides. Add '0.02894724152' to each side of the equation. 0.3402777778n + 0.02894724152 + n2 = -0.4166666667 + 0.02894724152 Reorder the terms: 0.02894724152 + 0.3402777778n + n2 = -0.4166666667 + 0.02894724152 Combine like terms: -0.4166666667 + 0.02894724152 = -0.38771942518 0.02894724152 + 0.3402777778n + n2 = -0.38771942518 Factor a perfect square on the left side: (n + 0.1701388889)(n + 0.1701388889) = -0.38771942518 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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