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Simplifying 7n2 + -5n + -4 = 0 Reorder the terms: -4 + -5n + 7n2 = 0 Solving -4 + -5n + 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'. -0.5714285714 + -0.7142857143n + n2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.7142857143n + 0.5714285714 + n2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.7142857143n + n2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.7142857143n + n2 = 0 + 0.5714285714 -0.7142857143n + n2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.7142857143n + n2 = 0.5714285714 The n term is -0.7142857143n. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143n + 0.1275510204 + n2 = 0.5714285714 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143n + n2 = 0.5714285714 + 0.1275510204 Combine like terms: 0.5714285714 + 0.1275510204 = 0.6989795918 0.1275510204 + -0.7142857143n + n2 = 0.6989795918 Factor a perfect square on the left side: (n + -0.3571428572)(n + -0.3571428572) = 0.6989795918 Calculate the square root of the right side: 0.836049994 Break this problem into two subproblems by setting (n + -0.3571428572) equal to 0.836049994 and -0.836049994.Subproblem 1
n + -0.3571428572 = 0.836049994 Simplifying n + -0.3571428572 = 0.836049994 Reorder the terms: -0.3571428572 + n = 0.836049994 Solving -0.3571428572 + n = 0.836049994 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + n = 0.836049994 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + n = 0.836049994 + 0.3571428572 n = 0.836049994 + 0.3571428572 Combine like terms: 0.836049994 + 0.3571428572 = 1.1931928512 n = 1.1931928512 Simplifying n = 1.1931928512Subproblem 2
n + -0.3571428572 = -0.836049994 Simplifying n + -0.3571428572 = -0.836049994 Reorder the terms: -0.3571428572 + n = -0.836049994 Solving -0.3571428572 + n = -0.836049994 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + n = -0.836049994 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + n = -0.836049994 + 0.3571428572 n = -0.836049994 + 0.3571428572 Combine like terms: -0.836049994 + 0.3571428572 = -0.4789071368 n = -0.4789071368 Simplifying n = -0.4789071368Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.1931928512, -0.4789071368}
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