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Simplifying (4n + -9n2 + -2) + (-4 + -6n + -12n2) = 0 Reorder the terms: (-2 + 4n + -9n2) + (-4 + -6n + -12n2) = 0 Remove parenthesis around (-2 + 4n + -9n2) -2 + 4n + -9n2 + (-4 + -6n + -12n2) = 0 Remove parenthesis around (-4 + -6n + -12n2) -2 + 4n + -9n2 + -4 + -6n + -12n2 = 0 Reorder the terms: -2 + -4 + 4n + -6n + -9n2 + -12n2 = 0 Combine like terms: -2 + -4 = -6 -6 + 4n + -6n + -9n2 + -12n2 = 0 Combine like terms: 4n + -6n = -2n -6 + -2n + -9n2 + -12n2 = 0 Combine like terms: -9n2 + -12n2 = -21n2 -6 + -2n + -21n2 = 0 Solving -6 + -2n + -21n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 2n + 21n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 2n + 21n2)' equal to zero and attempt to solve: Simplifying 6 + 2n + 21n2 = 0 Solving 6 + 2n + 21n2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.2857142857 + 0.09523809524n + n2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 0.09523809524n + -0.2857142857 + n2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 0.09523809524n + n2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 0.09523809524n + n2 = 0 + -0.2857142857 0.09523809524n + n2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 0.09523809524n + n2 = -0.2857142857 The n term is 0.09523809524n. Take half its coefficient (0.04761904762). Square it (0.002267573696) and add it to both sides. Add '0.002267573696' to each side of the equation. 0.09523809524n + 0.002267573696 + n2 = -0.2857142857 + 0.002267573696 Reorder the terms: 0.002267573696 + 0.09523809524n + n2 = -0.2857142857 + 0.002267573696 Combine like terms: -0.2857142857 + 0.002267573696 = -0.283446712004 0.002267573696 + 0.09523809524n + n2 = -0.283446712004 Factor a perfect square on the left side: (n + 0.04761904762)(n + 0.04761904762) = -0.283446712004 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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