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Simplifying 2n(4n + -6) + 9(6n + 8) = 0 Reorder the terms: 2n(-6 + 4n) + 9(6n + 8) = 0 (-6 * 2n + 4n * 2n) + 9(6n + 8) = 0 (-12n + 8n2) + 9(6n + 8) = 0 Reorder the terms: -12n + 8n2 + 9(8 + 6n) = 0 -12n + 8n2 + (8 * 9 + 6n * 9) = 0 -12n + 8n2 + (72 + 54n) = 0 Reorder the terms: 72 + -12n + 54n + 8n2 = 0 Combine like terms: -12n + 54n = 42n 72 + 42n + 8n2 = 0 Solving 72 + 42n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 21n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 21n + 4n2)' equal to zero and attempt to solve: Simplifying 36 + 21n + 4n2 = 0 Solving 36 + 21n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9 + 5.25n + n2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 5.25n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + 5.25n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5.25n + n2 = 0 + -9 5.25n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 5.25n + n2 = -9 The n term is 5.25n. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25n + 6.890625 + n2 = -9 + 6.890625 Reorder the terms: 6.890625 + 5.25n + n2 = -9 + 6.890625 Combine like terms: -9 + 6.890625 = -2.109375 6.890625 + 5.25n + n2 = -2.109375 Factor a perfect square on the left side: (n + 2.625)(n + 2.625) = -2.109375 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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