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Simplifying 10u2 + -5u + -4 = 0 Reorder the terms: -4 + -5u + 10u2 = 0 Solving -4 + -5u + 10u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + -0.5u + u2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.5u + 0.4 + u2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.5u + u2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.5u + u2 = 0 + 0.4 -0.5u + u2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.5u + u2 = 0.4 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 = 0.4 + 0.0625 Reorder the terms: 0.0625 + -0.5u + u2 = 0.4 + 0.0625 Combine like terms: 0.4 + 0.0625 = 0.4625 0.0625 + -0.5u + u2 = 0.4625 Factor a perfect square on the left side: (u + -0.25)(u + -0.25) = 0.4625 Calculate the square root of the right side: 0.680073525 Break this problem into two subproblems by setting (u + -0.25) equal to 0.680073525 and -0.680073525.Subproblem 1
u + -0.25 = 0.680073525 Simplifying u + -0.25 = 0.680073525 Reorder the terms: -0.25 + u = 0.680073525 Solving -0.25 + u = 0.680073525 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 = 0.680073525 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + u = 0.680073525 + 0.25 u = 0.680073525 + 0.25 Combine like terms: 0.680073525 + 0.25 = 0.930073525 u = 0.930073525 Simplifying u = 0.930073525Subproblem 2
u + -0.25 = -0.680073525 Simplifying u + -0.25 = -0.680073525 Reorder the terms: -0.25 + u = -0.680073525 Solving -0.25 + u = -0.680073525 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 = -0.680073525 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + u = -0.680073525 + 0.25 u = -0.680073525 + 0.25 Combine like terms: -0.680073525 + 0.25 = -0.430073525 u = -0.430073525 Simplifying u = -0.430073525Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.930073525, -0.430073525}
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