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Simplifying 5n2 + -30n = 100 Reorder the terms: -30n + 5n2 = 100 Solving -30n + 5n2 = 100 Solving for variable 'n'. Reorder the terms: -100 + -30n + 5n2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -30n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + -6n + n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + -6n + n2)' equal to zero and attempt to solve: Simplifying -20 + -6n + n2 = 0 Solving -20 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -6n + 20 + n2 = 0 + 20 Reorder the terms: -20 + 20 + -6n + n2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -6n + n2 = 0 + 20 -6n + n2 = 0 + 20 Combine like terms: 0 + 20 = 20 -6n + n2 = 20 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 20 + 9 Reorder the terms: 9 + -6n + n2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + -6n + n2 = 29 Factor a perfect square on the left side: (n + -3)(n + -3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (n + -3) equal to 5.385164807 and -5.385164807.Subproblem 1
n + -3 = 5.385164807 Simplifying n + -3 = 5.385164807 Reorder the terms: -3 + n = 5.385164807 Solving -3 + n = 5.385164807 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + n = 5.385164807 + 3 n = 5.385164807 + 3 Combine like terms: 5.385164807 + 3 = 8.385164807 n = 8.385164807 Simplifying n = 8.385164807Subproblem 2
n + -3 = -5.385164807 Simplifying n + -3 = -5.385164807 Reorder the terms: -3 + n = -5.385164807 Solving -3 + n = -5.385164807 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + n = -5.385164807 + 3 n = -5.385164807 + 3 Combine like terms: -5.385164807 + 3 = -2.385164807 n = -2.385164807 Simplifying n = -2.385164807Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.385164807, -2.385164807}Solution
n = {8.385164807, -2.385164807}
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