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Simplifying -12n2 + -9n + 2 = 7 Reorder the terms: 2 + -9n + -12n2 = 7 Solving 2 + -9n + -12n2 = 7 Solving for variable 'n'. Reorder the terms: 2 + -7 + -9n + -12n2 = 7 + -7 Combine like terms: 2 + -7 = -5 -5 + -9n + -12n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -5 + -9n + -12n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 9n + 12n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 9n + 12n2)' equal to zero and attempt to solve: Simplifying 5 + 9n + 12n2 = 0 Solving 5 + 9n + 12n2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + 0.75n + n2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 0.75n + -0.4166666667 + n2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 0.75n + n2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 0.75n + n2 = 0 + -0.4166666667 0.75n + n2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 0.75n + n2 = -0.4166666667 The n term is 0.75n. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75n + 0.140625 + n2 = -0.4166666667 + 0.140625 Reorder the terms: 0.140625 + 0.75n + n2 = -0.4166666667 + 0.140625 Combine like terms: -0.4166666667 + 0.140625 = -0.2760416667 0.140625 + 0.75n + n2 = -0.2760416667 Factor a perfect square on the left side: (n + 0.375)(n + 0.375) = -0.2760416667 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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