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Simplifying n2 + -2n = 357 Reorder the terms: -2n + n2 = 357 Solving -2n + n2 = 357 Solving for variable 'n'. Reorder the terms: -357 + -2n + n2 = 357 + -357 Combine like terms: 357 + -357 = 0 -357 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '357' to each side of the equation. -357 + -2n + 357 + n2 = 0 + 357 Reorder the terms: -357 + 357 + -2n + n2 = 0 + 357 Combine like terms: -357 + 357 = 0 0 + -2n + n2 = 0 + 357 -2n + n2 = 0 + 357 Combine like terms: 0 + 357 = 357 -2n + n2 = 357 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 357 + 1 Reorder the terms: 1 + -2n + n2 = 357 + 1 Combine like terms: 357 + 1 = 358 1 + -2n + n2 = 358 Factor a perfect square on the left side: (n + -1)(n + -1) = 358 Calculate the square root of the right side: 18.920887928 Break this problem into two subproblems by setting (n + -1) equal to 18.920887928 and -18.920887928.Subproblem 1
n + -1 = 18.920887928 Simplifying n + -1 = 18.920887928 Reorder the terms: -1 + n = 18.920887928 Solving -1 + n = 18.920887928 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 18.920887928 + 1 Combine like terms: -1 + 1 = 0 0 + n = 18.920887928 + 1 n = 18.920887928 + 1 Combine like terms: 18.920887928 + 1 = 19.920887928 n = 19.920887928 Simplifying n = 19.920887928Subproblem 2
n + -1 = -18.920887928 Simplifying n + -1 = -18.920887928 Reorder the terms: -1 + n = -18.920887928 Solving -1 + n = -18.920887928 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -18.920887928 + 1 Combine like terms: -1 + 1 = 0 0 + n = -18.920887928 + 1 n = -18.920887928 + 1 Combine like terms: -18.920887928 + 1 = -17.920887928 n = -17.920887928 Simplifying n = -17.920887928Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.920887928, -17.920887928}
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