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Simplifying 7n2 + -10n + -12 = 0 Reorder the terms: -12 + -10n + 7n2 = 0 Solving -12 + -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'. -1.714285714 + -1.428571429n + n2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -1.428571429n + 1.714285714 + n2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -1.428571429n + n2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -1.428571429n + n2 = 0 + 1.714285714 -1.428571429n + n2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -1.428571429n + n2 = 1.714285714 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 = 1.714285714 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429n + n2 = 1.714285714 + 0.5102040819 Combine like terms: 1.714285714 + 0.5102040819 = 2.2244897959 0.5102040819 + -1.428571429n + n2 = 2.2244897959 Factor a perfect square on the left side: (n + -0.7142857145)(n + -0.7142857145) = 2.2244897959 Calculate the square root of the right side: 1.491472358 Break this problem into two subproblems by setting (n + -0.7142857145) equal to 1.491472358 and -1.491472358.Subproblem 1
n + -0.7142857145 = 1.491472358 Simplifying n + -0.7142857145 = 1.491472358 Reorder the terms: -0.7142857145 + n = 1.491472358 Solving -0.7142857145 + n = 1.491472358 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 = 1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + n = 1.491472358 + 0.7142857145 n = 1.491472358 + 0.7142857145 Combine like terms: 1.491472358 + 0.7142857145 = 2.2057580725 n = 2.2057580725 Simplifying n = 2.2057580725Subproblem 2
n + -0.7142857145 = -1.491472358 Simplifying n + -0.7142857145 = -1.491472358 Reorder the terms: -0.7142857145 + n = -1.491472358 Solving -0.7142857145 + n = -1.491472358 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 = -1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + n = -1.491472358 + 0.7142857145 n = -1.491472358 + 0.7142857145 Combine like terms: -1.491472358 + 0.7142857145 = -0.7771866435 n = -0.7771866435 Simplifying n = -0.7771866435Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.2057580725, -0.7771866435}
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