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Simplifying 2n + -3n(4n + 5) = -6(n + -3) + -1 Reorder the terms: 2n + -3n(5 + 4n) = -6(n + -3) + -1 2n + (5 * -3n + 4n * -3n) = -6(n + -3) + -1 2n + (-15n + -12n2) = -6(n + -3) + -1 Combine like terms: 2n + -15n = -13n -13n + -12n2 = -6(n + -3) + -1 Reorder the terms: -13n + -12n2 = -6(-3 + n) + -1 -13n + -12n2 = (-3 * -6 + n * -6) + -1 -13n + -12n2 = (18 + -6n) + -1 Reorder the terms: -13n + -12n2 = 18 + -1 + -6n Combine like terms: 18 + -1 = 17 -13n + -12n2 = 17 + -6n Solving -13n + -12n2 = 17 + -6n Solving for variable 'n'. Reorder the terms: -17 + -13n + 6n + -12n2 = 17 + -6n + -17 + 6n Combine like terms: -13n + 6n = -7n -17 + -7n + -12n2 = 17 + -6n + -17 + 6n Reorder the terms: -17 + -7n + -12n2 = 17 + -17 + -6n + 6n Combine like terms: 17 + -17 = 0 -17 + -7n + -12n2 = 0 + -6n + 6n -17 + -7n + -12n2 = -6n + 6n Combine like terms: -6n + 6n = 0 -17 + -7n + -12n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 7n + 12n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 7n + 12n2)' equal to zero and attempt to solve: Simplifying 17 + 7n + 12n2 = 0 Solving 17 + 7n + 12n2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.416666667 + 0.5833333333n + n2 = 0 Move the constant term to the right: Add '-1.416666667' to each side of the equation. 1.416666667 + 0.5833333333n + -1.416666667 + n2 = 0 + -1.416666667 Reorder the terms: 1.416666667 + -1.416666667 + 0.5833333333n + n2 = 0 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + 0.5833333333n + n2 = 0 + -1.416666667 0.5833333333n + n2 = 0 + -1.416666667 Combine like terms: 0 + -1.416666667 = -1.416666667 0.5833333333n + n2 = -1.416666667 The n term is 0.5833333333n. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333n + 0.08506944446 + n2 = -1.416666667 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333n + n2 = -1.416666667 + 0.08506944446 Combine like terms: -1.416666667 + 0.08506944446 = -1.33159722254 0.08506944446 + 0.5833333333n + n2 = -1.33159722254 Factor a perfect square on the left side: (n + 0.2916666667)(n + 0.2916666667) = -1.33159722254 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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