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Simplifying 85n + -5n2 = 14400 Solving 85n + -5n2 = 14400 Solving for variable 'n'. Reorder the terms: -14400 + 85n + -5n2 = 14400 + -14400 Combine like terms: 14400 + -14400 = 0 -14400 + 85n + -5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2880 + 17n + -1n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2880 + 17n + -1n2)' equal to zero and attempt to solve: Simplifying -2880 + 17n + -1n2 = 0 Solving -2880 + 17n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2880 + -17n + n2 = 0 Move the constant term to the right: Add '-2880' to each side of the equation. 2880 + -17n + -2880 + n2 = 0 + -2880 Reorder the terms: 2880 + -2880 + -17n + n2 = 0 + -2880 Combine like terms: 2880 + -2880 = 0 0 + -17n + n2 = 0 + -2880 -17n + n2 = 0 + -2880 Combine like terms: 0 + -2880 = -2880 -17n + n2 = -2880 The n term is -17n. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17n + 72.25 + n2 = -2880 + 72.25 Reorder the terms: 72.25 + -17n + n2 = -2880 + 72.25 Combine like terms: -2880 + 72.25 = -2807.75 72.25 + -17n + n2 = -2807.75 Factor a perfect square on the left side: (n + -8.5)(n + -8.5) = -2807.75 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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