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Simplifying 10u2 + -2 = 5u Reorder the terms: -2 + 10u2 = 5u Solving -2 + 10u2 = 5u Solving for variable 'u'. Reorder the terms: -2 + -5u + 10u2 = 5u + -5u Combine like terms: 5u + -5u = 0 -2 + -5u + 10u2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -0.5u + u2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.5u + 0.2 + u2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.5u + u2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.5u + u2 = 0 + 0.2 -0.5u + u2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.5u + u2 = 0.2 The u term is -0.5u. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5u + 0.0625 + u2 = 0.2 + 0.0625 Reorder the terms: 0.0625 + -0.5u + u2 = 0.2 + 0.0625 Combine like terms: 0.2 + 0.0625 = 0.2625 0.0625 + -0.5u + u2 = 0.2625 Factor a perfect square on the left side: (u + -0.25)(u + -0.25) = 0.2625 Calculate the square root of the right side: 0.512347538 Break this problem into two subproblems by setting (u + -0.25) equal to 0.512347538 and -0.512347538.Subproblem 1
u + -0.25 = 0.512347538 Simplifying u + -0.25 = 0.512347538 Reorder the terms: -0.25 + u = 0.512347538 Solving -0.25 + u = 0.512347538 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + u = 0.512347538 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + u = 0.512347538 + 0.25 u = 0.512347538 + 0.25 Combine like terms: 0.512347538 + 0.25 = 0.762347538 u = 0.762347538 Simplifying u = 0.762347538Subproblem 2
u + -0.25 = -0.512347538 Simplifying u + -0.25 = -0.512347538 Reorder the terms: -0.25 + u = -0.512347538 Solving -0.25 + u = -0.512347538 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + u = -0.512347538 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + u = -0.512347538 + 0.25 u = -0.512347538 + 0.25 Combine like terms: -0.512347538 + 0.25 = -0.262347538 u = -0.262347538 Simplifying u = -0.262347538Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.762347538, -0.262347538}
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