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Simplifying 8n + -3n(3n + 8) = 12 Reorder the terms: 8n + -3n(8 + 3n) = 12 8n + (8 * -3n + 3n * -3n) = 12 8n + (-24n + -9n2) = 12 Combine like terms: 8n + -24n = -16n -16n + -9n2 = 12 Solving -16n + -9n2 = 12 Solving for variable 'n'. Reorder the terms: -12 + -16n + -9n2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -16n + -9n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 16n + 9n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 16n + 9n2)' equal to zero and attempt to solve: Simplifying 12 + 16n + 9n2 = 0 Solving 12 + 16n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.333333333 + 1.777777778n + n2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.777777778n + -1.333333333 + n2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.777777778n + n2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.777777778n + n2 = 0 + -1.333333333 1.777777778n + n2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.777777778n + n2 = -1.333333333 The n term is 1.777777778n. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778n + 0.7901234570 + n2 = -1.333333333 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778n + n2 = -1.333333333 + 0.7901234570 Combine like terms: -1.333333333 + 0.7901234570 = -0.543209876 0.7901234570 + 1.777777778n + n2 = -0.543209876 Factor a perfect square on the left side: (n + 0.888888889)(n + 0.888888889) = -0.543209876 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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