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Simplifying 7n2 + 4n + -40 = 0 Reorder the terms: -40 + 4n + 7n2 = 0 Solving -40 + 4n + 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'. -5.714285714 + 0.5714285714n + n2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + 0.5714285714n + 5.714285714 + n2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + 0.5714285714n + n2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + 0.5714285714n + n2 = 0 + 5.714285714 0.5714285714n + n2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 0.5714285714n + n2 = 5.714285714 The n term is 0.5714285714n. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714n + 0.08163265305 + n2 = 5.714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714n + n2 = 5.714285714 + 0.08163265305 Combine like terms: 5.714285714 + 0.08163265305 = 5.79591836705 0.08163265305 + 0.5714285714n + n2 = 5.79591836705 Factor a perfect square on the left side: (n + 0.2857142857)(n + 0.2857142857) = 5.79591836705 Calculate the square root of the right side: 2.407471364 Break this problem into two subproblems by setting (n + 0.2857142857) equal to 2.407471364 and -2.407471364.Subproblem 1
n + 0.2857142857 = 2.407471364 Simplifying n + 0.2857142857 = 2.407471364 Reorder the terms: 0.2857142857 + n = 2.407471364 Solving 0.2857142857 + n = 2.407471364 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + n = 2.407471364 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + n = 2.407471364 + -0.2857142857 n = 2.407471364 + -0.2857142857 Combine like terms: 2.407471364 + -0.2857142857 = 2.1217570783 n = 2.1217570783 Simplifying n = 2.1217570783Subproblem 2
n + 0.2857142857 = -2.407471364 Simplifying n + 0.2857142857 = -2.407471364 Reorder the terms: 0.2857142857 + n = -2.407471364 Solving 0.2857142857 + n = -2.407471364 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + n = -2.407471364 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + n = -2.407471364 + -0.2857142857 n = -2.407471364 + -0.2857142857 Combine like terms: -2.407471364 + -0.2857142857 = -2.6931856497 n = -2.6931856497 Simplifying n = -2.6931856497Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.1217570783, -2.6931856497}
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