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Simplifying 6n2 = -8n + -10 Reorder the terms: 6n2 = -10 + -8n Solving 6n2 = -10 + -8n Solving for variable 'n'. Reorder the terms: 10 + 8n + 6n2 = -10 + -8n + 10 + 8n Reorder the terms: 10 + 8n + 6n2 = -10 + 10 + -8n + 8n Combine like terms: -10 + 10 = 0 10 + 8n + 6n2 = 0 + -8n + 8n 10 + 8n + 6n2 = -8n + 8n Combine like terms: -8n + 8n = 0 10 + 8n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 4n + 3n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 4n + 3n2)' equal to zero and attempt to solve: Simplifying 5 + 4n + 3n2 = 0 Solving 5 + 4n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 1.333333333n + n2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.333333333n + -1.666666667 + n2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.333333333n + n2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.333333333n + n2 = 0 + -1.666666667 1.333333333n + n2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.333333333n + n2 = -1.666666667 The n term is 1.333333333n. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333n + 0.4444444442 + n2 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333n + n2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + 1.333333333n + n2 = -1.2222222228 Factor a perfect square on the left side: (n + 0.6666666665)(n + 0.6666666665) = -1.2222222228 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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