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Simplifying -8n2 + 10n + 6 = 10 Reorder the terms: 6 + 10n + -8n2 = 10 Solving 6 + 10n + -8n2 = 10 Solving for variable 'n'. Reorder the terms: 6 + -10 + 10n + -8n2 = 10 + -10 Combine like terms: 6 + -10 = -4 -4 + 10n + -8n2 = 10 + -10 Combine like terms: 10 + -10 = 0 -4 + 10n + -8n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 5n + -4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 5n + -4n2)' equal to zero and attempt to solve: Simplifying -2 + 5n + -4n2 = 0 Solving -2 + 5n + -4n2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.5 + -1.25n + n2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.25n + -0.5 + n2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.25n + n2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.25n + n2 = 0 + -0.5 -1.25n + n2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.25n + n2 = -0.5 The n term is -1.25n. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25n + 0.390625 + n2 = -0.5 + 0.390625 Reorder the terms: 0.390625 + -1.25n + n2 = -0.5 + 0.390625 Combine like terms: -0.5 + 0.390625 = -0.109375 0.390625 + -1.25n + n2 = -0.109375 Factor a perfect square on the left side: (n + -0.625)(n + -0.625) = -0.109375 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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