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Simplifying 2u2 + 7u + -28 = 0 Reorder the terms: -28 + 7u + 2u2 = 0 Solving -28 + 7u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 3.5u + u2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 3.5u + 14 + u2 = 0 + 14 Reorder the terms: -14 + 14 + 3.5u + u2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 3.5u + u2 = 0 + 14 3.5u + u2 = 0 + 14 Combine like terms: 0 + 14 = 14 3.5u + u2 = 14 The u term is 3.5u. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5u + 3.0625 + u2 = 14 + 3.0625 Reorder the terms: 3.0625 + 3.5u + u2 = 14 + 3.0625 Combine like terms: 14 + 3.0625 = 17.0625 3.0625 + 3.5u + u2 = 17.0625 Factor a perfect square on the left side: (u + 1.75)(u + 1.75) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (u + 1.75) equal to 4.13067791 and -4.13067791.Subproblem 1
u + 1.75 = 4.13067791 Simplifying u + 1.75 = 4.13067791 Reorder the terms: 1.75 + u = 4.13067791 Solving 1.75 + u = 4.13067791 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + u = 4.13067791 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + u = 4.13067791 + -1.75 u = 4.13067791 + -1.75 Combine like terms: 4.13067791 + -1.75 = 2.38067791 u = 2.38067791 Simplifying u = 2.38067791Subproblem 2
u + 1.75 = -4.13067791 Simplifying u + 1.75 = -4.13067791 Reorder the terms: 1.75 + u = -4.13067791 Solving 1.75 + u = -4.13067791 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + u = -4.13067791 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + u = -4.13067791 + -1.75 u = -4.13067791 + -1.75 Combine like terms: -4.13067791 + -1.75 = -5.88067791 u = -5.88067791 Simplifying u = -5.88067791Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.38067791, -5.88067791}
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