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Simplifying 4n2 + -10n + 34 = 0 Reorder the terms: 34 + -10n + 4n2 = 0 Solving 34 + -10n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -5n + 2n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -5n + 2n2)' equal to zero and attempt to solve: Simplifying 17 + -5n + 2n2 = 0 Solving 17 + -5n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -2.5n + n2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -2.5n + -8.5 + n2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -2.5n + n2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -2.5n + n2 = 0 + -8.5 -2.5n + n2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -2.5n + n2 = -8.5 The n term is -2.5n. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5n + 1.5625 + n2 = -8.5 + 1.5625 Reorder the terms: 1.5625 + -2.5n + n2 = -8.5 + 1.5625 Combine like terms: -8.5 + 1.5625 = -6.9375 1.5625 + -2.5n + n2 = -6.9375 Factor a perfect square on the left side: (n + -1.25)(n + -1.25) = -6.9375 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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