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Simplifying 5u2 + 7u = 2 Reorder the terms: 7u + 5u2 = 2 Solving 7u + 5u2 = 2 Solving for variable 'u'. Reorder the terms: -2 + 7u + 5u2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 7u + 5u2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 1.4u + u2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.4u + 0.4 + u2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.4u + u2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.4u + u2 = 0 + 0.4 1.4u + u2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.4u + u2 = 0.4 The u term is 1.4u. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4u + 0.49 + u2 = 0.4 + 0.49 Reorder the terms: 0.49 + 1.4u + u2 = 0.4 + 0.49 Combine like terms: 0.4 + 0.49 = 0.89 0.49 + 1.4u + u2 = 0.89 Factor a perfect square on the left side: (u + 0.7)(u + 0.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (u + 0.7) equal to 0.943398113 and -0.943398113.Subproblem 1
u + 0.7 = 0.943398113 Simplifying u + 0.7 = 0.943398113 Reorder the terms: 0.7 + u = 0.943398113 Solving 0.7 + u = 0.943398113 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + u = 0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + u = 0.943398113 + -0.7 u = 0.943398113 + -0.7 Combine like terms: 0.943398113 + -0.7 = 0.243398113 u = 0.243398113 Simplifying u = 0.243398113Subproblem 2
u + 0.7 = -0.943398113 Simplifying u + 0.7 = -0.943398113 Reorder the terms: 0.7 + u = -0.943398113 Solving 0.7 + u = -0.943398113 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + u = -0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + u = -0.943398113 + -0.7 u = -0.943398113 + -0.7 Combine like terms: -0.943398113 + -0.7 = -1.643398113 u = -1.643398113 Simplifying u = -1.643398113Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.243398113, -1.643398113}
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