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Simplifying -24n(3n + -6) + -2 = 238 Reorder the terms: -24n(-6 + 3n) + -2 = 238 (-6 * -24n + 3n * -24n) + -2 = 238 (144n + -72n2) + -2 = 238 Reorder the terms: -2 + 144n + -72n2 = 238 Solving -2 + 144n + -72n2 = 238 Solving for variable 'n'. Reorder the terms: -2 + -238 + 144n + -72n2 = 238 + -238 Combine like terms: -2 + -238 = -240 -240 + 144n + -72n2 = 238 + -238 Combine like terms: 238 + -238 = 0 -240 + 144n + -72n2 = 0 Factor out the Greatest Common Factor (GCF), '24'. 24(-10 + 6n + -3n2) = 0 Ignore the factor 24.Subproblem 1
Set the factor '(-10 + 6n + -3n2)' equal to zero and attempt to solve: Simplifying -10 + 6n + -3n2 = 0 Solving -10 + 6n + -3n2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 3.333333333 + -2n + n2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -2n + -3.333333333 + n2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -2n + n2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -2n + n2 = 0 + -3.333333333 -2n + n2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -2n + n2 = -3.333333333 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = -3.333333333 + 1 Reorder the terms: 1 + -2n + n2 = -3.333333333 + 1 Combine like terms: -3.333333333 + 1 = -2.333333333 1 + -2n + n2 = -2.333333333 Factor a perfect square on the left side: (n + -1)(n + -1) = -2.333333333 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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