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Simplifying 6n2 + 12 = 9n Reorder the terms: 12 + 6n2 = 9n Solving 12 + 6n2 = 9n Solving for variable 'n'. Reorder the terms: 12 + -9n + 6n2 = 9n + -9n Combine like terms: 9n + -9n = 0 12 + -9n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -3n + 2n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -3n + 2n2)' equal to zero and attempt to solve: Simplifying 4 + -3n + 2n2 = 0 Solving 4 + -3n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -1.5n + n2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.5n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -1.5n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.5n + n2 = 0 + -2 -1.5n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.5n + n2 = -2 The n term is -1.5n. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5n + 0.5625 + n2 = -2 + 0.5625 Reorder the terms: 0.5625 + -1.5n + n2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + -1.5n + n2 = -1.4375 Factor a perfect square on the left side: (n + -0.75)(n + -0.75) = -1.4375 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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