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Simplifying 4n2 + 24n + -2200 = 0 Reorder the terms: -2200 + 24n + 4n2 = 0 Solving -2200 + 24n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-550 + 6n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-550 + 6n + n2)' equal to zero and attempt to solve: Simplifying -550 + 6n + n2 = 0 Solving -550 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '550' to each side of the equation. -550 + 6n + 550 + n2 = 0 + 550 Reorder the terms: -550 + 550 + 6n + n2 = 0 + 550 Combine like terms: -550 + 550 = 0 0 + 6n + n2 = 0 + 550 6n + n2 = 0 + 550 Combine like terms: 0 + 550 = 550 6n + n2 = 550 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 = 550 + 9 Reorder the terms: 9 + 6n + n2 = 550 + 9 Combine like terms: 550 + 9 = 559 9 + 6n + n2 = 559 Factor a perfect square on the left side: (n + 3)(n + 3) = 559 Calculate the square root of the right side: 23.643180835 Break this problem into two subproblems by setting (n + 3) equal to 23.643180835 and -23.643180835.Subproblem 1
n + 3 = 23.643180835 Simplifying n + 3 = 23.643180835 Reorder the terms: 3 + n = 23.643180835 Solving 3 + n = 23.643180835 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 = 23.643180835 + -3 Combine like terms: 3 + -3 = 0 0 + n = 23.643180835 + -3 n = 23.643180835 + -3 Combine like terms: 23.643180835 + -3 = 20.643180835 n = 20.643180835 Simplifying n = 20.643180835Subproblem 2
n + 3 = -23.643180835 Simplifying n + 3 = -23.643180835 Reorder the terms: 3 + n = -23.643180835 Solving 3 + n = -23.643180835 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 = -23.643180835 + -3 Combine like terms: 3 + -3 = 0 0 + n = -23.643180835 + -3 n = -23.643180835 + -3 Combine like terms: -23.643180835 + -3 = -26.643180835 n = -26.643180835 Simplifying n = -26.643180835Solution
The solution to the problem is based on the solutions from the subproblems. n = {20.643180835, -26.643180835}Solution
n = {20.643180835, -26.643180835}
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