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Simplifying 39 + 3n = -12n2 + 1 + 5n Reorder the terms: 39 + 3n = 1 + 5n + -12n2 Solving 39 + 3n = 1 + 5n + -12n2 Solving for variable 'n'. Reorder the terms: 39 + -1 + 3n + -5n + 12n2 = 1 + 5n + -12n2 + -1 + -5n + 12n2 Combine like terms: 39 + -1 = 38 38 + 3n + -5n + 12n2 = 1 + 5n + -12n2 + -1 + -5n + 12n2 Combine like terms: 3n + -5n = -2n 38 + -2n + 12n2 = 1 + 5n + -12n2 + -1 + -5n + 12n2 Reorder the terms: 38 + -2n + 12n2 = 1 + -1 + 5n + -5n + -12n2 + 12n2 Combine like terms: 1 + -1 = 0 38 + -2n + 12n2 = 0 + 5n + -5n + -12n2 + 12n2 38 + -2n + 12n2 = 5n + -5n + -12n2 + 12n2 Combine like terms: 5n + -5n = 0 38 + -2n + 12n2 = 0 + -12n2 + 12n2 38 + -2n + 12n2 = -12n2 + 12n2 Combine like terms: -12n2 + 12n2 = 0 38 + -2n + 12n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -1n + 6n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -1n + 6n2)' equal to zero and attempt to solve: Simplifying 19 + -1n + 6n2 = 0 Solving 19 + -1n + 6n2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.166666667 + -0.1666666667n + n2 = 0 Move the constant term to the right: Add '-3.166666667' to each side of the equation. 3.166666667 + -0.1666666667n + -3.166666667 + n2 = 0 + -3.166666667 Reorder the terms: 3.166666667 + -3.166666667 + -0.1666666667n + n2 = 0 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + -0.1666666667n + n2 = 0 + -3.166666667 -0.1666666667n + n2 = 0 + -3.166666667 Combine like terms: 0 + -3.166666667 = -3.166666667 -0.1666666667n + n2 = -3.166666667 The n term is -0.1666666667n. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667n + 0.006944444447 + n2 = -3.166666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667n + n2 = -3.166666667 + 0.006944444447 Combine like terms: -3.166666667 + 0.006944444447 = -3.159722222553 0.006944444447 + -0.1666666667n + n2 = -3.159722222553 Factor a perfect square on the left side: (n + -0.08333333335)(n + -0.08333333335) = -3.159722222553 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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