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Simplifying 4n2 + 4n = -24 Reorder the terms: 4n + 4n2 = -24 Solving 4n + 4n2 = -24 Solving for variable 'n'. Reorder the terms: 24 + 4n + 4n2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 4n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(6 + n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + n + n2)' equal to zero and attempt to solve: Simplifying 6 + n + n2 = 0 Solving 6 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + n + n2 = 0 + -6 n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 n + n2 = -6 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = -6 + 0.25 Reorder the terms: 0.25 + n + n2 = -6 + 0.25 Combine like terms: -6 + 0.25 = -5.75 0.25 + n + n2 = -5.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -5.75 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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