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Simplifying 6n2 + 24n + 72 = 0 Reorder the terms: 72 + 24n + 6n2 = 0 Solving 72 + 24n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(12 + 4n + n2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(12 + 4n + n2)' equal to zero and attempt to solve: Simplifying 12 + 4n + n2 = 0 Solving 12 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 4n + -12 + n2 = 0 + -12 Reorder the terms: 12 + -12 + 4n + n2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 4n + n2 = 0 + -12 4n + n2 = 0 + -12 Combine like terms: 0 + -12 = -12 4n + n2 = -12 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = -12 + 4 Reorder the terms: 4 + 4n + n2 = -12 + 4 Combine like terms: -12 + 4 = -8 4 + 4n + n2 = -8 Factor a perfect square on the left side: (n + 2)(n + 2) = -8 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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