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Simplifying 5n2 + 30n = 25 Reorder the terms: 30n + 5n2 = 25 Solving 30n + 5n2 = 25 Solving for variable 'n'. Reorder the terms: -25 + 30n + 5n2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 30n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + 6n + n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + 6n + n2)' equal to zero and attempt to solve: Simplifying -5 + 6n + n2 = 0 Solving -5 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 6n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + 6n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6n + n2 = 0 + 5 6n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 6n + n2 = 5 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 = 5 + 9 Reorder the terms: 9 + 6n + n2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6n + n2 = 14 Factor a perfect square on the left side: (n + 3)(n + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (n + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
n + 3 = 3.741657387 Simplifying n + 3 = 3.741657387 Reorder the terms: 3 + n = 3.741657387 Solving 3 + n = 3.741657387 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 = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + n = 3.741657387 + -3 n = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 n = 0.741657387 Simplifying n = 0.741657387Subproblem 2
n + 3 = -3.741657387 Simplifying n + 3 = -3.741657387 Reorder the terms: 3 + n = -3.741657387 Solving 3 + n = -3.741657387 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 = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + n = -3.741657387 + -3 n = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 n = -6.741657387 Simplifying n = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.741657387, -6.741657387}Solution
n = {0.741657387, -6.741657387}
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