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Simplifying 6n2 + -87n + 240 = 0 Reorder the terms: 240 + -87n + 6n2 = 0 Solving 240 + -87n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(80 + -29n + 2n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(80 + -29n + 2n2)' equal to zero and attempt to solve: Simplifying 80 + -29n + 2n2 = 0 Solving 80 + -29n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 40 + -14.5n + n2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -14.5n + -40 + n2 = 0 + -40 Reorder the terms: 40 + -40 + -14.5n + n2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -14.5n + n2 = 0 + -40 -14.5n + n2 = 0 + -40 Combine like terms: 0 + -40 = -40 -14.5n + n2 = -40 The n term is -14.5n. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5n + 52.5625 + n2 = -40 + 52.5625 Reorder the terms: 52.5625 + -14.5n + n2 = -40 + 52.5625 Combine like terms: -40 + 52.5625 = 12.5625 52.5625 + -14.5n + n2 = 12.5625 Factor a perfect square on the left side: (n + -7.25)(n + -7.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (n + -7.25) equal to 3.54436172 and -3.54436172.Subproblem 1
n + -7.25 = 3.54436172 Simplifying n + -7.25 = 3.54436172 Reorder the terms: -7.25 + n = 3.54436172 Solving -7.25 + n = 3.54436172 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + n = 3.54436172 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + n = 3.54436172 + 7.25 n = 3.54436172 + 7.25 Combine like terms: 3.54436172 + 7.25 = 10.79436172 n = 10.79436172 Simplifying n = 10.79436172Subproblem 2
n + -7.25 = -3.54436172 Simplifying n + -7.25 = -3.54436172 Reorder the terms: -7.25 + n = -3.54436172 Solving -7.25 + n = -3.54436172 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + n = -3.54436172 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + n = -3.54436172 + 7.25 n = -3.54436172 + 7.25 Combine like terms: -3.54436172 + 7.25 = 3.70563828 n = 3.70563828 Simplifying n = 3.70563828Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.79436172, 3.70563828}Solution
n = {10.79436172, 3.70563828}
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