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Simplifying 2n2 + 2n + 18 = 0 Reorder the terms: 18 + 2n + 2n2 = 0 Solving 18 + 2n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + n + n2)' equal to zero and attempt to solve: Simplifying 9 + n + n2 = 0 Solving 9 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + n + n2 = 0 + -9 n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 n + n2 = -9 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 = -9 + 0.25 Reorder the terms: 0.25 + n + n2 = -9 + 0.25 Combine like terms: -9 + 0.25 = -8.75 0.25 + n + n2 = -8.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -8.75 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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