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Simplifying 10n2 + -10n + 16 = 0 Reorder the terms: 16 + -10n + 10n2 = 0 Solving 16 + -10n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -5n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -5n + 5n2)' equal to zero and attempt to solve: Simplifying 8 + -5n + 5n2 = 0 Solving 8 + -5n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -1n + n2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -1n + -1.6 + n2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -1n + n2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -1n + n2 = 0 + -1.6 -1n + n2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -1n + n2 = -1.6 The n term is -1n. 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. -1n + 0.25 + n2 = -1.6 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -1.6 + 0.25 Combine like terms: -1.6 + 0.25 = -1.35 0.25 + -1n + n2 = -1.35 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = -1.35 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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