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Simplifying 9(n2 + n + 2) = 0 Reorder the terms: 9(2 + n + n2) = 0 (2 * 9 + n * 9 + n2 * 9) = 0 (18 + 9n + 9n2) = 0 Solving 18 + 9n + 9n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '9'. 9(2 + n + n2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(2 + n + n2)' equal to zero and attempt to solve: Simplifying 2 + n + n2 = 0 Solving 2 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n + n2 = 0 + -2 n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 n + n2 = -2 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 = -2 + 0.25 Reorder the terms: 0.25 + n + n2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + n + n2 = -1.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -1.75 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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