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Simplifying 4n2 + 8n + 60 = 0 Reorder the terms: 60 + 8n + 4n2 = 0 Solving 60 + 8n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + 2n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + 2n + n2)' equal to zero and attempt to solve: Simplifying 15 + 2n + n2 = 0 Solving 15 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 2n + -15 + n2 = 0 + -15 Reorder the terms: 15 + -15 + 2n + n2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2n + n2 = 0 + -15 2n + n2 = 0 + -15 Combine like terms: 0 + -15 = -15 2n + n2 = -15 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 = -15 + 1 Reorder the terms: 1 + 2n + n2 = -15 + 1 Combine like terms: -15 + 1 = -14 1 + 2n + n2 = -14 Factor a perfect square on the left side: (n + 1)(n + 1) = -14 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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