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Simplifying 10 + 4(8 + 9n2) + 3n = 0 10 + (8 * 4 + 9n2 * 4) + 3n = 0 10 + (32 + 36n2) + 3n = 0 Reorder the terms: 10 + 32 + 3n + 36n2 = 0 Combine like terms: 10 + 32 = 42 42 + 3n + 36n2 = 0 Solving 42 + 3n + 36n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + n + 12n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + n + 12n2)' equal to zero and attempt to solve: Simplifying 14 + n + 12n2 = 0 Solving 14 + n + 12n2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.166666667 + 0.08333333333n + n2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 0.08333333333n + -1.166666667 + n2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 0.08333333333n + n2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 0.08333333333n + n2 = 0 + -1.166666667 0.08333333333n + n2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 0.08333333333n + n2 = -1.166666667 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. 0.08333333333n + 0.25 + n2 = -1.166666667 + 0.25 Reorder the terms: 0.25 + 0.08333333333n + n2 = -1.166666667 + 0.25 Combine like terms: -1.166666667 + 0.25 = -0.916666667 0.25 + 0.08333333333n + n2 = -0.916666667 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -0.916666667 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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