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Simplifying 8n2 + -4n + 18 = 0 Reorder the terms: 18 + -4n + 8n2 = 0 Solving 18 + -4n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -2n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -2n + 4n2)' equal to zero and attempt to solve: Simplifying 9 + -2n + 4n2 = 0 Solving 9 + -2n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -0.5n + n2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -0.5n + -2.25 + n2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -0.5n + n2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -0.5n + n2 = 0 + -2.25 -0.5n + n2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -0.5n + n2 = -2.25 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = -2.25 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = -2.25 + 0.0625 Combine like terms: -2.25 + 0.0625 = -2.1875 0.0625 + -0.5n + n2 = -2.1875 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = -2.1875 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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