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Simplifying n2 + -1n + -16290 = 0 Reorder the terms: -16290 + -1n + n2 = 0 Solving -16290 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '16290' to each side of the equation. -16290 + -1n + 16290 + n2 = 0 + 16290 Reorder the terms: -16290 + 16290 + -1n + n2 = 0 + 16290 Combine like terms: -16290 + 16290 = 0 0 + -1n + n2 = 0 + 16290 -1n + n2 = 0 + 16290 Combine like terms: 0 + 16290 = 16290 -1n + n2 = 16290 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 16290 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 16290 + 0.25 Combine like terms: 16290 + 0.25 = 16290.25 0.25 + -1n + n2 = 16290.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 16290.25 Calculate the square root of the right side: 127.633263689 Break this problem into two subproblems by setting (n + -0.5) equal to 127.633263689 and -127.633263689.Subproblem 1
n + -0.5 = 127.633263689 Simplifying n + -0.5 = 127.633263689 Reorder the terms: -0.5 + n = 127.633263689 Solving -0.5 + n = 127.633263689 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 127.633263689 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 127.633263689 + 0.5 n = 127.633263689 + 0.5 Combine like terms: 127.633263689 + 0.5 = 128.133263689 n = 128.133263689 Simplifying n = 128.133263689Subproblem 2
n + -0.5 = -127.633263689 Simplifying n + -0.5 = -127.633263689 Reorder the terms: -0.5 + n = -127.633263689 Solving -0.5 + n = -127.633263689 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -127.633263689 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -127.633263689 + 0.5 n = -127.633263689 + 0.5 Combine like terms: -127.633263689 + 0.5 = -127.133263689 n = -127.133263689 Simplifying n = -127.133263689Solution
The solution to the problem is based on the solutions from the subproblems. n = {128.133263689, -127.133263689}
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