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Simplifying 10n2 + -2n + 8 = 0 Reorder the terms: 8 + -2n + 10n2 = 0 Solving 8 + -2n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -1n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1n + 5n2)' equal to zero and attempt to solve: Simplifying 4 + -1n + 5n2 = 0 Solving 4 + -1n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -0.2n + n2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -0.2n + -0.8 + n2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -0.2n + n2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -0.2n + n2 = 0 + -0.8 -0.2n + n2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -0.2n + n2 = -0.8 The n term is -0.2n. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2n + 0.01 + n2 = -0.8 + 0.01 Reorder the terms: 0.01 + -0.2n + n2 = -0.8 + 0.01 Combine like terms: -0.8 + 0.01 = -0.79 0.01 + -0.2n + n2 = -0.79 Factor a perfect square on the left side: (n + -0.1)(n + -0.1) = -0.79 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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