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Simplifying 2n(n + -3) = -12 Reorder the terms: 2n(-3 + n) = -12 (-3 * 2n + n * 2n) = -12 (-6n + 2n2) = -12 Solving -6n + 2n2 = -12 Solving for variable 'n'. Reorder the terms: 12 + -6n + 2n2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -6n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -3n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -3n + n2)' equal to zero and attempt to solve: Simplifying 6 + -3n + n2 = 0 Solving 6 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -3n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + -3n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -3n + n2 = 0 + -6 -3n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 -3n + n2 = -6 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = -6 + 2.25 Reorder the terms: 2.25 + -3n + n2 = -6 + 2.25 Combine like terms: -6 + 2.25 = -3.75 2.25 + -3n + n2 = -3.75 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = -3.75 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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