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Simplifying -25n2 + 57n = -14 Reorder the terms: 57n + -25n2 = -14 Solving 57n + -25n2 = -14 Solving for variable 'n'. Reorder the terms: 14 + 57n + -25n2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + 57n + -25n2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.56 + -2.28n + n2 = 0 Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + -2.28n + 0.56 + n2 = 0 + 0.56 Reorder the terms: -0.56 + 0.56 + -2.28n + n2 = 0 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + -2.28n + n2 = 0 + 0.56 -2.28n + n2 = 0 + 0.56 Combine like terms: 0 + 0.56 = 0.56 -2.28n + n2 = 0.56 The n term is -2.28n. Take half its coefficient (-1.14). Square it (1.2996) and add it to both sides. Add '1.2996' to each side of the equation. -2.28n + 1.2996 + n2 = 0.56 + 1.2996 Reorder the terms: 1.2996 + -2.28n + n2 = 0.56 + 1.2996 Combine like terms: 0.56 + 1.2996 = 1.8596 1.2996 + -2.28n + n2 = 1.8596 Factor a perfect square on the left side: (n + -1.14)(n + -1.14) = 1.8596 Calculate the square root of the right side: 1.363671515 Break this problem into two subproblems by setting (n + -1.14) equal to 1.363671515 and -1.363671515.Subproblem 1
n + -1.14 = 1.363671515 Simplifying n + -1.14 = 1.363671515 Reorder the terms: -1.14 + n = 1.363671515 Solving -1.14 + n = 1.363671515 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.14' to each side of the equation. -1.14 + 1.14 + n = 1.363671515 + 1.14 Combine like terms: -1.14 + 1.14 = 0.00 0.00 + n = 1.363671515 + 1.14 n = 1.363671515 + 1.14 Combine like terms: 1.363671515 + 1.14 = 2.503671515 n = 2.503671515 Simplifying n = 2.503671515Subproblem 2
n + -1.14 = -1.363671515 Simplifying n + -1.14 = -1.363671515 Reorder the terms: -1.14 + n = -1.363671515 Solving -1.14 + n = -1.363671515 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.14' to each side of the equation. -1.14 + 1.14 + n = -1.363671515 + 1.14 Combine like terms: -1.14 + 1.14 = 0.00 0.00 + n = -1.363671515 + 1.14 n = -1.363671515 + 1.14 Combine like terms: -1.363671515 + 1.14 = -0.223671515 n = -0.223671515 Simplifying n = -0.223671515Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.503671515, -0.223671515}
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