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Simplifying 8n2 + 16n + 14 = 0 Reorder the terms: 14 + 16n + 8n2 = 0 Solving 14 + 16n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 8n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 8n + 4n2)' equal to zero and attempt to solve: Simplifying 7 + 8n + 4n2 = 0 Solving 7 + 8n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 2n + n2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 2n + -1.75 + n2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 2n + n2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 2n + n2 = 0 + -1.75 2n + n2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 2n + n2 = -1.75 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = -1.75 + 1 Reorder the terms: 1 + 2n + n2 = -1.75 + 1 Combine like terms: -1.75 + 1 = -0.75 1 + 2n + n2 = -0.75 Factor a perfect square on the left side: (n + 1)(n + 1) = -0.75 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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