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Simplifying 2u2 + 17u + 14 = 0 Reorder the terms: 14 + 17u + 2u2 = 0 Solving 14 + 17u + 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'. 7 + 8.5u + u2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 8.5u + -7 + u2 = 0 + -7 Reorder the terms: 7 + -7 + 8.5u + u2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8.5u + u2 = 0 + -7 8.5u + u2 = 0 + -7 Combine like terms: 0 + -7 = -7 8.5u + u2 = -7 The u term is 8.5u. 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. 8.5u + 18.0625 + u2 = -7 + 18.0625 Reorder the terms: 18.0625 + 8.5u + u2 = -7 + 18.0625 Combine like terms: -7 + 18.0625 = 11.0625 18.0625 + 8.5u + u2 = 11.0625 Factor a perfect square on the left side: (u + 4.25)(u + 4.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (u + 4.25) equal to 3.326033674 and -3.326033674.Subproblem 1
u + 4.25 = 3.326033674 Simplifying u + 4.25 = 3.326033674 Reorder the terms: 4.25 + u = 3.326033674 Solving 4.25 + u = 3.326033674 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + u = 3.326033674 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + u = 3.326033674 + -4.25 u = 3.326033674 + -4.25 Combine like terms: 3.326033674 + -4.25 = -0.923966326 u = -0.923966326 Simplifying u = -0.923966326Subproblem 2
u + 4.25 = -3.326033674 Simplifying u + 4.25 = -3.326033674 Reorder the terms: 4.25 + u = -3.326033674 Solving 4.25 + u = -3.326033674 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + u = -3.326033674 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + u = -3.326033674 + -4.25 u = -3.326033674 + -4.25 Combine like terms: -3.326033674 + -4.25 = -7.576033674 u = -7.576033674 Simplifying u = -7.576033674Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.923966326, -7.576033674}
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