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Simplifying 5n2 + -30n + 16 = 0 Reorder the terms: 16 + -30n + 5n2 = 0 Solving 16 + -30n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -6n + n2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -6n + -3.2 + n2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -6n + n2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -6n + n2 = 0 + -3.2 -6n + n2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -6n + n2 = -3.2 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 = -3.2 + 9 Reorder the terms: 9 + -6n + n2 = -3.2 + 9 Combine like terms: -3.2 + 9 = 5.8 9 + -6n + n2 = 5.8 Factor a perfect square on the left side: (n + -3)(n + -3) = 5.8 Calculate the square root of the right side: 2.408318916 Break this problem into two subproblems by setting (n + -3) equal to 2.408318916 and -2.408318916.Subproblem 1
n + -3 = 2.408318916 Simplifying n + -3 = 2.408318916 Reorder the terms: -3 + n = 2.408318916 Solving -3 + n = 2.408318916 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 = 2.408318916 + 3 Combine like terms: -3 + 3 = 0 0 + n = 2.408318916 + 3 n = 2.408318916 + 3 Combine like terms: 2.408318916 + 3 = 5.408318916 n = 5.408318916 Simplifying n = 5.408318916Subproblem 2
n + -3 = -2.408318916 Simplifying n + -3 = -2.408318916 Reorder the terms: -3 + n = -2.408318916 Solving -3 + n = -2.408318916 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 = -2.408318916 + 3 Combine like terms: -3 + 3 = 0 0 + n = -2.408318916 + 3 n = -2.408318916 + 3 Combine like terms: -2.408318916 + 3 = 0.591681084 n = 0.591681084 Simplifying n = 0.591681084Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.408318916, 0.591681084}
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