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Simplifying 38 + 8n = -6n(1 + 6n) 38 + 8n = (1 * -6n + 6n * -6n) 38 + 8n = (-6n + -36n2) Solving 38 + 8n = -6n + -36n2 Solving for variable 'n'. Combine like terms: 8n + 6n = 14n 38 + 14n + 36n2 = -6n + -36n2 + 6n + 36n2 Reorder the terms: 38 + 14n + 36n2 = -6n + 6n + -36n2 + 36n2 Combine like terms: -6n + 6n = 0 38 + 14n + 36n2 = 0 + -36n2 + 36n2 38 + 14n + 36n2 = -36n2 + 36n2 Combine like terms: -36n2 + 36n2 = 0 38 + 14n + 36n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + 7n + 18n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + 7n + 18n2)' equal to zero and attempt to solve: Simplifying 19 + 7n + 18n2 = 0 Solving 19 + 7n + 18n2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 1.055555556 + 0.3888888889n + n2 = 0 Move the constant term to the right: Add '-1.055555556' to each side of the equation. 1.055555556 + 0.3888888889n + -1.055555556 + n2 = 0 + -1.055555556 Reorder the terms: 1.055555556 + -1.055555556 + 0.3888888889n + n2 = 0 + -1.055555556 Combine like terms: 1.055555556 + -1.055555556 = 0.000000000 0.000000000 + 0.3888888889n + n2 = 0 + -1.055555556 0.3888888889n + n2 = 0 + -1.055555556 Combine like terms: 0 + -1.055555556 = -1.055555556 0.3888888889n + n2 = -1.055555556 The n term is 0.3888888889n. Take half its coefficient (0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. 0.3888888889n + 0.03780864200 + n2 = -1.055555556 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889n + n2 = -1.055555556 + 0.03780864200 Combine like terms: -1.055555556 + 0.03780864200 = -1.017746914 0.03780864200 + 0.3888888889n + n2 = -1.017746914 Factor a perfect square on the left side: (n + 0.1944444445)(n + 0.1944444445) = -1.017746914 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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