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Simplifying 2u2 + 7u = 3 Reorder the terms: 7u + 2u2 = 3 Solving 7u + 2u2 = 3 Solving for variable 'u'. Reorder the terms: -3 + 7u + 2u2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 7u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 3.5u + u2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 3.5u + 1.5 + u2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 3.5u + u2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 3.5u + u2 = 0 + 1.5 3.5u + u2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 3.5u + u2 = 1.5 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 = 1.5 + 3.0625 Reorder the terms: 3.0625 + 3.5u + u2 = 1.5 + 3.0625 Combine like terms: 1.5 + 3.0625 = 4.5625 3.0625 + 3.5u + u2 = 4.5625 Factor a perfect square on the left side: (u + 1.75)(u + 1.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (u + 1.75) equal to 2.136000936 and -2.136000936.Subproblem 1
u + 1.75 = 2.136000936 Simplifying u + 1.75 = 2.136000936 Reorder the terms: 1.75 + u = 2.136000936 Solving 1.75 + u = 2.136000936 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 = 2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + u = 2.136000936 + -1.75 u = 2.136000936 + -1.75 Combine like terms: 2.136000936 + -1.75 = 0.386000936 u = 0.386000936 Simplifying u = 0.386000936Subproblem 2
u + 1.75 = -2.136000936 Simplifying u + 1.75 = -2.136000936 Reorder the terms: 1.75 + u = -2.136000936 Solving 1.75 + u = -2.136000936 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 = -2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + u = -2.136000936 + -1.75 u = -2.136000936 + -1.75 Combine like terms: -2.136000936 + -1.75 = -3.886000936 u = -3.886000936 Simplifying u = -3.886000936Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.386000936, -3.886000936}
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