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Simplifying 10n2 + 4n + 2 = 0 Reorder the terms: 2 + 4n + 10n2 = 0 Solving 2 + 4n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 2n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 2n + 5n2)' equal to zero and attempt to solve: Simplifying 1 + 2n + 5n2 = 0 Solving 1 + 2n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 0.4n + n2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 0.4n + -0.2 + n2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 0.4n + n2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.4n + n2 = 0 + -0.2 0.4n + n2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 0.4n + n2 = -0.2 The n term is 0.4n. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4n + 0.04 + n2 = -0.2 + 0.04 Reorder the terms: 0.04 + 0.4n + n2 = -0.2 + 0.04 Combine like terms: -0.2 + 0.04 = -0.16 0.04 + 0.4n + n2 = -0.16 Factor a perfect square on the left side: (n + 0.2)(n + 0.2) = -0.16 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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