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Simplifying 5u2 + -34u + 36 = 0 Reorder the terms: 36 + -34u + 5u2 = 0 Solving 36 + -34u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.2 + -6.8u + u2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -6.8u + -7.2 + u2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -6.8u + u2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -6.8u + u2 = 0 + -7.2 -6.8u + u2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -6.8u + u2 = -7.2 The u term is -6.8u. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8u + 11.56 + u2 = -7.2 + 11.56 Reorder the terms: 11.56 + -6.8u + u2 = -7.2 + 11.56 Combine like terms: -7.2 + 11.56 = 4.36 11.56 + -6.8u + u2 = 4.36 Factor a perfect square on the left side: (u + -3.4)(u + -3.4) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (u + -3.4) equal to 2.088061302 and -2.088061302.Subproblem 1
u + -3.4 = 2.088061302 Simplifying u + -3.4 = 2.088061302 Reorder the terms: -3.4 + u = 2.088061302 Solving -3.4 + u = 2.088061302 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + u = 2.088061302 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + u = 2.088061302 + 3.4 u = 2.088061302 + 3.4 Combine like terms: 2.088061302 + 3.4 = 5.488061302 u = 5.488061302 Simplifying u = 5.488061302Subproblem 2
u + -3.4 = -2.088061302 Simplifying u + -3.4 = -2.088061302 Reorder the terms: -3.4 + u = -2.088061302 Solving -3.4 + u = -2.088061302 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + u = -2.088061302 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + u = -2.088061302 + 3.4 u = -2.088061302 + 3.4 Combine like terms: -2.088061302 + 3.4 = 1.311938698 u = 1.311938698 Simplifying u = 1.311938698Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.488061302, 1.311938698}
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