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Simplifying 3n2 + -27n + 432 = 0 Reorder the terms: 432 + -27n + 3n2 = 0 Solving 432 + -27n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(144 + -9n + n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(144 + -9n + n2)' equal to zero and attempt to solve: Simplifying 144 + -9n + n2 = 0 Solving 144 + -9n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -9n + -144 + n2 = 0 + -144 Reorder the terms: 144 + -144 + -9n + n2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -9n + n2 = 0 + -144 -9n + n2 = 0 + -144 Combine like terms: 0 + -144 = -144 -9n + n2 = -144 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = -144 + 20.25 Reorder the terms: 20.25 + -9n + n2 = -144 + 20.25 Combine like terms: -144 + 20.25 = -123.75 20.25 + -9n + n2 = -123.75 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = -123.75 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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