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Simplifying -10n + 3(8 + 8n) = -6n(n + -4) -10n + (8 * 3 + 8n * 3) = -6n(n + -4) -10n + (24 + 24n) = -6n(n + -4) Reorder the terms: 24 + -10n + 24n = -6n(n + -4) Combine like terms: -10n + 24n = 14n 24 + 14n = -6n(n + -4) Reorder the terms: 24 + 14n = -6n(-4 + n) 24 + 14n = (-4 * -6n + n * -6n) 24 + 14n = (24n + -6n2) Solving 24 + 14n = 24n + -6n2 Solving for variable 'n'. Combine like terms: 14n + -24n = -10n 24 + -10n + 6n2 = 24n + -6n2 + -24n + 6n2 Reorder the terms: 24 + -10n + 6n2 = 24n + -24n + -6n2 + 6n2 Combine like terms: 24n + -24n = 0 24 + -10n + 6n2 = 0 + -6n2 + 6n2 24 + -10n + 6n2 = -6n2 + 6n2 Combine like terms: -6n2 + 6n2 = 0 24 + -10n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -5n + 3n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -5n + 3n2)' equal to zero and attempt to solve: Simplifying 12 + -5n + 3n2 = 0 Solving 12 + -5n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -1.666666667n + n2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1.666666667n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + -1.666666667n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1.666666667n + n2 = 0 + -4 -1.666666667n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1.666666667n + n2 = -4 The n term is -1.666666667n. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667n + 0.6944444447 + n2 = -4 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667n + n2 = -4 + 0.6944444447 Combine like terms: -4 + 0.6944444447 = -3.3055555553 0.6944444447 + -1.666666667n + n2 = -3.3055555553 Factor a perfect square on the left side: (n + -0.8333333335)(n + -0.8333333335) = -3.3055555553 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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