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Simplifying 7n2 + -10n + 2 = 0 Reorder the terms: 2 + -10n + 7n2 = 0 Solving 2 + -10n + 7n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + -1.428571429n + n2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -1.428571429n + -0.2857142857 + n2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -1.428571429n + n2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -1.428571429n + n2 = 0 + -0.2857142857 -1.428571429n + n2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -1.428571429n + n2 = -0.2857142857 The n term is -1.428571429n. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429n + 0.5102040819 + n2 = -0.2857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429n + n2 = -0.2857142857 + 0.5102040819 Combine like terms: -0.2857142857 + 0.5102040819 = 0.2244897962 0.5102040819 + -1.428571429n + n2 = 0.2244897962 Factor a perfect square on the left side: (n + -0.7142857145)(n + -0.7142857145) = 0.2244897962 Calculate the square root of the right side: 0.473803542 Break this problem into two subproblems by setting (n + -0.7142857145) equal to 0.473803542 and -0.473803542.Subproblem 1
n + -0.7142857145 = 0.473803542 Simplifying n + -0.7142857145 = 0.473803542 Reorder the terms: -0.7142857145 + n = 0.473803542 Solving -0.7142857145 + n = 0.473803542 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + n = 0.473803542 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + n = 0.473803542 + 0.7142857145 n = 0.473803542 + 0.7142857145 Combine like terms: 0.473803542 + 0.7142857145 = 1.1880892565 n = 1.1880892565 Simplifying n = 1.1880892565Subproblem 2
n + -0.7142857145 = -0.473803542 Simplifying n + -0.7142857145 = -0.473803542 Reorder the terms: -0.7142857145 + n = -0.473803542 Solving -0.7142857145 + n = -0.473803542 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + n = -0.473803542 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + n = -0.473803542 + 0.7142857145 n = -0.473803542 + 0.7142857145 Combine like terms: -0.473803542 + 0.7142857145 = 0.2404821725 n = 0.2404821725 Simplifying n = 0.2404821725Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.1880892565, 0.2404821725}
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