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Simplifying 2n2 + 17n + -28 = 0 Reorder the terms: -28 + 17n + 2n2 = 0 Solving -28 + 17n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 8.5n + n2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 8.5n + 14 + n2 = 0 + 14 Reorder the terms: -14 + 14 + 8.5n + n2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 8.5n + n2 = 0 + 14 8.5n + n2 = 0 + 14 Combine like terms: 0 + 14 = 14 8.5n + n2 = 14 The n term is 8.5n. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5n + 18.0625 + n2 = 14 + 18.0625 Reorder the terms: 18.0625 + 8.5n + n2 = 14 + 18.0625 Combine like terms: 14 + 18.0625 = 32.0625 18.0625 + 8.5n + n2 = 32.0625 Factor a perfect square on the left side: (n + 4.25)(n + 4.25) = 32.0625 Calculate the square root of the right side: 5.662375826 Break this problem into two subproblems by setting (n + 4.25) equal to 5.662375826 and -5.662375826.Subproblem 1
n + 4.25 = 5.662375826 Simplifying n + 4.25 = 5.662375826 Reorder the terms: 4.25 + n = 5.662375826 Solving 4.25 + n = 5.662375826 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + n = 5.662375826 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + n = 5.662375826 + -4.25 n = 5.662375826 + -4.25 Combine like terms: 5.662375826 + -4.25 = 1.412375826 n = 1.412375826 Simplifying n = 1.412375826Subproblem 2
n + 4.25 = -5.662375826 Simplifying n + 4.25 = -5.662375826 Reorder the terms: 4.25 + n = -5.662375826 Solving 4.25 + n = -5.662375826 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + n = -5.662375826 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + n = -5.662375826 + -4.25 n = -5.662375826 + -4.25 Combine like terms: -5.662375826 + -4.25 = -9.912375826 n = -9.912375826 Simplifying n = -9.912375826Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.412375826, -9.912375826}
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