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Simplifying n2 + -3n + -77 = 0 Reorder the terms: -77 + -3n + n2 = 0 Solving -77 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -3n + 77 + n2 = 0 + 77 Reorder the terms: -77 + 77 + -3n + n2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -3n + n2 = 0 + 77 -3n + n2 = 0 + 77 Combine like terms: 0 + 77 = 77 -3n + n2 = 77 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 77 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 77 + 2.25 Combine like terms: 77 + 2.25 = 79.25 2.25 + -3n + n2 = 79.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (n + -1.5) equal to 8.902246907 and -8.902246907.Subproblem 1
n + -1.5 = 8.902246907 Simplifying n + -1.5 = 8.902246907 Reorder the terms: -1.5 + n = 8.902246907 Solving -1.5 + n = 8.902246907 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 8.902246907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 8.902246907 + 1.5 n = 8.902246907 + 1.5 Combine like terms: 8.902246907 + 1.5 = 10.402246907 n = 10.402246907 Simplifying n = 10.402246907Subproblem 2
n + -1.5 = -8.902246907 Simplifying n + -1.5 = -8.902246907 Reorder the terms: -1.5 + n = -8.902246907 Solving -1.5 + n = -8.902246907 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -8.902246907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -8.902246907 + 1.5 n = -8.902246907 + 1.5 Combine like terms: -8.902246907 + 1.5 = -7.402246907 n = -7.402246907 Simplifying n = -7.402246907Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.402246907, -7.402246907}
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