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Simplifying 8n2 + -35n + -40 = 0 Reorder the terms: -40 + -35n + 8n2 = 0 Solving -40 + -35n + 8n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5 + -4.375n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.375n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -4.375n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.375n + n2 = 0 + 5 -4.375n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.375n + n2 = 5 The n term is -4.375n. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375n + 4.78515625 + n2 = 5 + 4.78515625 Reorder the terms: 4.78515625 + -4.375n + n2 = 5 + 4.78515625 Combine like terms: 5 + 4.78515625 = 9.78515625 4.78515625 + -4.375n + n2 = 9.78515625 Factor a perfect square on the left side: (n + -2.1875)(n + -2.1875) = 9.78515625 Calculate the square root of the right side: 3.128123439 Break this problem into two subproblems by setting (n + -2.1875) equal to 3.128123439 and -3.128123439.Subproblem 1
n + -2.1875 = 3.128123439 Simplifying n + -2.1875 = 3.128123439 Reorder the terms: -2.1875 + n = 3.128123439 Solving -2.1875 + n = 3.128123439 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + n = 3.128123439 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + n = 3.128123439 + 2.1875 n = 3.128123439 + 2.1875 Combine like terms: 3.128123439 + 2.1875 = 5.315623439 n = 5.315623439 Simplifying n = 5.315623439Subproblem 2
n + -2.1875 = -3.128123439 Simplifying n + -2.1875 = -3.128123439 Reorder the terms: -2.1875 + n = -3.128123439 Solving -2.1875 + n = -3.128123439 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + n = -3.128123439 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + n = -3.128123439 + 2.1875 n = -3.128123439 + 2.1875 Combine like terms: -3.128123439 + 2.1875 = -0.940623439 n = -0.940623439 Simplifying n = -0.940623439Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.315623439, -0.940623439}
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