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Simplifying 2n2 + 13n + -28 = 0 Reorder the terms: -28 + 13n + 2n2 = 0 Solving -28 + 13n + 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 + 6.5n + n2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 6.5n + 14 + n2 = 0 + 14 Reorder the terms: -14 + 14 + 6.5n + n2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 6.5n + n2 = 0 + 14 6.5n + n2 = 0 + 14 Combine like terms: 0 + 14 = 14 6.5n + n2 = 14 The n term is 6.5n. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5n + 10.5625 + n2 = 14 + 10.5625 Reorder the terms: 10.5625 + 6.5n + n2 = 14 + 10.5625 Combine like terms: 14 + 10.5625 = 24.5625 10.5625 + 6.5n + n2 = 24.5625 Factor a perfect square on the left side: (n + 3.25)(n + 3.25) = 24.5625 Calculate the square root of the right side: 4.9560569 Break this problem into two subproblems by setting (n + 3.25) equal to 4.9560569 and -4.9560569.Subproblem 1
n + 3.25 = 4.9560569 Simplifying n + 3.25 = 4.9560569 Reorder the terms: 3.25 + n = 4.9560569 Solving 3.25 + n = 4.9560569 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + n = 4.9560569 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + n = 4.9560569 + -3.25 n = 4.9560569 + -3.25 Combine like terms: 4.9560569 + -3.25 = 1.7060569 n = 1.7060569 Simplifying n = 1.7060569Subproblem 2
n + 3.25 = -4.9560569 Simplifying n + 3.25 = -4.9560569 Reorder the terms: 3.25 + n = -4.9560569 Solving 3.25 + n = -4.9560569 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + n = -4.9560569 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + n = -4.9560569 + -3.25 n = -4.9560569 + -3.25 Combine like terms: -4.9560569 + -3.25 = -8.2060569 n = -8.2060569 Simplifying n = -8.2060569Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.7060569, -8.2060569}
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