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Simplifying 4n2 + 28n + 320 = 0 Reorder the terms: 320 + 28n + 4n2 = 0 Solving 320 + 28n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(80 + 7n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(80 + 7n + n2)' equal to zero and attempt to solve: Simplifying 80 + 7n + n2 = 0 Solving 80 + 7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 7n + -80 + n2 = 0 + -80 Reorder the terms: 80 + -80 + 7n + n2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 7n + n2 = 0 + -80 7n + n2 = 0 + -80 Combine like terms: 0 + -80 = -80 7n + n2 = -80 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = -80 + 12.25 Reorder the terms: 12.25 + 7n + n2 = -80 + 12.25 Combine like terms: -80 + 12.25 = -67.75 12.25 + 7n + n2 = -67.75 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = -67.75 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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