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Simplifying -8n2 + -2n + 3 = 4 Reorder the terms: 3 + -2n + -8n2 = 4 Solving 3 + -2n + -8n2 = 4 Solving for variable 'n'. Reorder the terms: 3 + -4 + -2n + -8n2 = 4 + -4 Combine like terms: 3 + -4 = -1 -1 + -2n + -8n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -1 + -2n + -8n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 2n + 8n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 2n + 8n2)' equal to zero and attempt to solve: Simplifying 1 + 2n + 8n2 = 0 Solving 1 + 2n + 8n2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 0.25n + n2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 0.25n + -0.125 + n2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 0.25n + n2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 0.25n + n2 = 0 + -0.125 0.25n + n2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 0.25n + n2 = -0.125 The n term is 0.25n. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25n + 0.015625 + n2 = -0.125 + 0.015625 Reorder the terms: 0.015625 + 0.25n + n2 = -0.125 + 0.015625 Combine like terms: -0.125 + 0.015625 = -0.109375 0.015625 + 0.25n + n2 = -0.109375 Factor a perfect square on the left side: (n + 0.125)(n + 0.125) = -0.109375 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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