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Simplifying 3n(35 + -4n) = 89n + 45 (35 * 3n + -4n * 3n) = 89n + 45 (105n + -12n2) = 89n + 45 Reorder the terms: 105n + -12n2 = 45 + 89n Solving 105n + -12n2 = 45 + 89n Solving for variable 'n'. Reorder the terms: -45 + 105n + -89n + -12n2 = 45 + 89n + -45 + -89n Combine like terms: 105n + -89n = 16n -45 + 16n + -12n2 = 45 + 89n + -45 + -89n Reorder the terms: -45 + 16n + -12n2 = 45 + -45 + 89n + -89n Combine like terms: 45 + -45 = 0 -45 + 16n + -12n2 = 0 + 89n + -89n -45 + 16n + -12n2 = 89n + -89n Combine like terms: 89n + -89n = 0 -45 + 16n + -12n2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 3.75 + -1.333333333n + n2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -1.333333333n + -3.75 + n2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -1.333333333n + n2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -1.333333333n + n2 = 0 + -3.75 -1.333333333n + n2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -1.333333333n + n2 = -3.75 The n term is -1.333333333n. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333n + 0.4444444442 + n2 = -3.75 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333n + n2 = -3.75 + 0.4444444442 Combine like terms: -3.75 + 0.4444444442 = -3.3055555558 0.4444444442 + -1.333333333n + n2 = -3.3055555558 Factor a perfect square on the left side: (n + -0.6666666665)(n + -0.6666666665) = -3.3055555558 Can't calculate square root of the right side. The solution to this equation could not be determined.
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