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Simplifying 5n2 + 100 = 300n Reorder the terms: 100 + 5n2 = 300n Solving 100 + 5n2 = 300n Solving for variable 'n'. Reorder the terms: 100 + -300n + 5n2 = 300n + -300n Combine like terms: 300n + -300n = 0 100 + -300n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(20 + -60n + n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(20 + -60n + n2)' equal to zero and attempt to solve: Simplifying 20 + -60n + n2 = 0 Solving 20 + -60n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -60n + -20 + n2 = 0 + -20 Reorder the terms: 20 + -20 + -60n + n2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -60n + n2 = 0 + -20 -60n + n2 = 0 + -20 Combine like terms: 0 + -20 = -20 -60n + n2 = -20 The n term is -60n. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60n + 900 + n2 = -20 + 900 Reorder the terms: 900 + -60n + n2 = -20 + 900 Combine like terms: -20 + 900 = 880 900 + -60n + n2 = 880 Factor a perfect square on the left side: (n + -30)(n + -30) = 880 Calculate the square root of the right side: 29.664793948 Break this problem into two subproblems by setting (n + -30) equal to 29.664793948 and -29.664793948.Subproblem 1
n + -30 = 29.664793948 Simplifying n + -30 = 29.664793948 Reorder the terms: -30 + n = 29.664793948 Solving -30 + n = 29.664793948 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + n = 29.664793948 + 30 Combine like terms: -30 + 30 = 0 0 + n = 29.664793948 + 30 n = 29.664793948 + 30 Combine like terms: 29.664793948 + 30 = 59.664793948 n = 59.664793948 Simplifying n = 59.664793948Subproblem 2
n + -30 = -29.664793948 Simplifying n + -30 = -29.664793948 Reorder the terms: -30 + n = -29.664793948 Solving -30 + n = -29.664793948 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + n = -29.664793948 + 30 Combine like terms: -30 + 30 = 0 0 + n = -29.664793948 + 30 n = -29.664793948 + 30 Combine like terms: -29.664793948 + 30 = 0.335206052 n = 0.335206052 Simplifying n = 0.335206052Solution
The solution to the problem is based on the solutions from the subproblems. n = {59.664793948, 0.335206052}Solution
n = {59.664793948, 0.335206052}
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