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Simplifying n2 + -9n + -552 = 0 Reorder the terms: -552 + -9n + n2 = 0 Solving -552 + -9n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '552' to each side of the equation. -552 + -9n + 552 + n2 = 0 + 552 Reorder the terms: -552 + 552 + -9n + n2 = 0 + 552 Combine like terms: -552 + 552 = 0 0 + -9n + n2 = 0 + 552 -9n + n2 = 0 + 552 Combine like terms: 0 + 552 = 552 -9n + n2 = 552 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 552 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 552 + 20.25 Combine like terms: 552 + 20.25 = 572.25 20.25 + -9n + n2 = 572.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 572.25 Calculate the square root of the right side: 23.921747428 Break this problem into two subproblems by setting (n + -4.5) equal to 23.921747428 and -23.921747428.Subproblem 1
n + -4.5 = 23.921747428 Simplifying n + -4.5 = 23.921747428 Reorder the terms: -4.5 + n = 23.921747428 Solving -4.5 + n = 23.921747428 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 23.921747428 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 23.921747428 + 4.5 n = 23.921747428 + 4.5 Combine like terms: 23.921747428 + 4.5 = 28.421747428 n = 28.421747428 Simplifying n = 28.421747428Subproblem 2
n + -4.5 = -23.921747428 Simplifying n + -4.5 = -23.921747428 Reorder the terms: -4.5 + n = -23.921747428 Solving -4.5 + n = -23.921747428 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -23.921747428 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -23.921747428 + 4.5 n = -23.921747428 + 4.5 Combine like terms: -23.921747428 + 4.5 = -19.421747428 n = -19.421747428 Simplifying n = -19.421747428Solution
The solution to the problem is based on the solutions from the subproblems. n = {28.421747428, -19.421747428}
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