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Simplifying -12n2 + -4n + -10 = 0 Reorder the terms: -10 + -4n + -12n2 = 0 Solving -10 + -4n + -12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 2n + 6n2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 2n + 6n2)' equal to zero and attempt to solve: Simplifying 5 + 2n + 6n2 = 0 Solving 5 + 2n + 6n2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.3333333333n + n2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.3333333333n + -0.8333333333 + n2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.3333333333n + n2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.3333333333n + n2 = 0 + -0.8333333333 0.3333333333n + n2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.3333333333n + n2 = -0.8333333333 The n term is 0.3333333333n. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333n + 0.02777777779 + n2 = -0.8333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333n + n2 = -0.8333333333 + 0.02777777779 Combine like terms: -0.8333333333 + 0.02777777779 = -0.80555555551 0.02777777779 + 0.3333333333n + n2 = -0.80555555551 Factor a perfect square on the left side: (n + 0.1666666667)(n + 0.1666666667) = -0.80555555551 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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