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Simplifying 15n + -1(3n + -5)(4n + 5) = 5 + -12n * 12n Reorder the terms: 15n + -1(-5 + 3n)(4n + 5) = 5 + -12n * 12n Reorder the terms: 15n + -1(-5 + 3n)(5 + 4n) = 5 + -12n * 12n Multiply (-5 + 3n) * (5 + 4n) 15n + -1(-5(5 + 4n) + 3n * (5 + 4n)) = 5 + -12n * 12n 15n + -1((5 * -5 + 4n * -5) + 3n * (5 + 4n)) = 5 + -12n * 12n 15n + -1((-25 + -20n) + 3n * (5 + 4n)) = 5 + -12n * 12n 15n + -1(-25 + -20n + (5 * 3n + 4n * 3n)) = 5 + -12n * 12n 15n + -1(-25 + -20n + (15n + 12n2)) = 5 + -12n * 12n Combine like terms: -20n + 15n = -5n 15n + -1(-25 + -5n + 12n2) = 5 + -12n * 12n 15n + (-25 * -1 + -5n * -1 + 12n2 * -1) = 5 + -12n * 12n 15n + (25 + 5n + -12n2) = 5 + -12n * 12n Reorder the terms: 25 + 15n + 5n + -12n2 = 5 + -12n * 12n Combine like terms: 15n + 5n = 20n 25 + 20n + -12n2 = 5 + -12n * 12n Reorder the terms for easier multiplication: 25 + 20n + -12n2 = 5 + -12 * 12n * n Multiply -12 * 12 25 + 20n + -12n2 = 5 + -144n * n Multiply n * n 25 + 20n + -12n2 = 5 + -144n2 Solving 25 + 20n + -12n2 = 5 + -144n2 Solving for variable 'n'. Reorder the terms: 25 + -5 + 20n + -12n2 + 144n2 = 5 + -144n2 + -5 + 144n2 Combine like terms: 25 + -5 = 20 20 + 20n + -12n2 + 144n2 = 5 + -144n2 + -5 + 144n2 Combine like terms: -12n2 + 144n2 = 132n2 20 + 20n + 132n2 = 5 + -144n2 + -5 + 144n2 Reorder the terms: 20 + 20n + 132n2 = 5 + -5 + -144n2 + 144n2 Combine like terms: 5 + -5 = 0 20 + 20n + 132n2 = 0 + -144n2 + 144n2 20 + 20n + 132n2 = -144n2 + 144n2 Combine like terms: -144n2 + 144n2 = 0 20 + 20n + 132n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 5n + 33n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 5n + 33n2)' equal to zero and attempt to solve: Simplifying 5 + 5n + 33n2 = 0 Solving 5 + 5n + 33n2 = 0 Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. 0.1515151515 + 0.1515151515n + n2 = 0 Move the constant term to the right: Add '-0.1515151515' to each side of the equation. 0.1515151515 + 0.1515151515n + -0.1515151515 + n2 = 0 + -0.1515151515 Reorder the terms: 0.1515151515 + -0.1515151515 + 0.1515151515n + n2 = 0 + -0.1515151515 Combine like terms: 0.1515151515 + -0.1515151515 = 0.0000000000 0.0000000000 + 0.1515151515n + n2 = 0 + -0.1515151515 0.1515151515n + n2 = 0 + -0.1515151515 Combine like terms: 0 + -0.1515151515 = -0.1515151515 0.1515151515n + n2 = -0.1515151515 The n term is 0.1515151515n. Take half its coefficient (0.07575757575). Square it (0.005739210284) and add it to both sides. Add '0.005739210284' to each side of the equation. 0.1515151515n + 0.005739210284 + n2 = -0.1515151515 + 0.005739210284 Reorder the terms: 0.005739210284 + 0.1515151515n + n2 = -0.1515151515 + 0.005739210284 Combine like terms: -0.1515151515 + 0.005739210284 = -0.145775941216 0.005739210284 + 0.1515151515n + n2 = -0.145775941216 Factor a perfect square on the left side: (n + 0.07575757575)(n + 0.07575757575) = -0.145775941216 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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