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Simplifying 12(4 + n) * 5(-2n + -9) = 18 Reorder the terms: 12(4 + n) * 5(-9 + -2n) = 18 Reorder the terms for easier multiplication: 12 * 5(4 + n)(-9 + -2n) = 18 Multiply 12 * 5 60(4 + n)(-9 + -2n) = 18 Multiply (4 + n) * (-9 + -2n) 60(4(-9 + -2n) + n(-9 + -2n)) = 18 60((-9 * 4 + -2n * 4) + n(-9 + -2n)) = 18 60((-36 + -8n) + n(-9 + -2n)) = 18 60(-36 + -8n + (-9 * n + -2n * n)) = 18 60(-36 + -8n + (-9n + -2n2)) = 18 Combine like terms: -8n + -9n = -17n 60(-36 + -17n + -2n2) = 18 (-36 * 60 + -17n * 60 + -2n2 * 60) = 18 (-2160 + -1020n + -120n2) = 18 Solving -2160 + -1020n + -120n2 = 18 Solving for variable 'n'. Reorder the terms: -2160 + -18 + -1020n + -120n2 = 18 + -18 Combine like terms: -2160 + -18 = -2178 -2178 + -1020n + -120n2 = 18 + -18 Combine like terms: 18 + -18 = 0 -2178 + -1020n + -120n2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(363 + 170n + 20n2) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(363 + 170n + 20n2)' equal to zero and attempt to solve: Simplifying 363 + 170n + 20n2 = 0 Solving 363 + 170n + 20n2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 18.15 + 8.5n + n2 = 0.0 Move the constant term to the right: Add '-18.15' to each side of the equation. 18.15 + 8.5n + -18.15 + n2 = 0.0 + -18.15 Reorder the terms: 18.15 + -18.15 + 8.5n + n2 = 0.0 + -18.15 Combine like terms: 18.15 + -18.15 = 0.00 0.00 + 8.5n + n2 = 0.0 + -18.15 8.5n + n2 = 0.0 + -18.15 Combine like terms: 0.0 + -18.15 = -18.15 8.5n + n2 = -18.15 The n term is 8.5n. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5n + 18.0625 + n2 = -18.15 + 18.0625 Reorder the terms: 18.0625 + 8.5n + n2 = -18.15 + 18.0625 Combine like terms: -18.15 + 18.0625 = -0.0875 18.0625 + 8.5n + n2 = -0.0875 Factor a perfect square on the left side: (n + 4.25)(n + 4.25) = -0.0875 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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