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Simplifying 2u2 = 4u + 1 Reorder the terms: 2u2 = 1 + 4u Solving 2u2 = 1 + 4u Solving for variable 'u'. Reorder the terms: -1 + -4u + 2u2 = 1 + 4u + -1 + -4u Reorder the terms: -1 + -4u + 2u2 = 1 + -1 + 4u + -4u Combine like terms: 1 + -1 = 0 -1 + -4u + 2u2 = 0 + 4u + -4u -1 + -4u + 2u2 = 4u + -4u Combine like terms: 4u + -4u = 0 -1 + -4u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2u + u2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2u + 0.5 + u2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2u + u2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2u + u2 = 0 + 0.5 -2u + u2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2u + u2 = 0.5 The u term is -2u. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2u + 1 + u2 = 0.5 + 1 Reorder the terms: 1 + -2u + u2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + -2u + u2 = 1.5 Factor a perfect square on the left side: (u + -1)(u + -1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (u + -1) equal to 1.224744871 and -1.224744871.Subproblem 1
u + -1 = 1.224744871 Simplifying u + -1 = 1.224744871 Reorder the terms: -1 + u = 1.224744871 Solving -1 + u = 1.224744871 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = 1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + u = 1.224744871 + 1 u = 1.224744871 + 1 Combine like terms: 1.224744871 + 1 = 2.224744871 u = 2.224744871 Simplifying u = 2.224744871Subproblem 2
u + -1 = -1.224744871 Simplifying u + -1 = -1.224744871 Reorder the terms: -1 + u = -1.224744871 Solving -1 + u = -1.224744871 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = -1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + u = -1.224744871 + 1 u = -1.224744871 + 1 Combine like terms: -1.224744871 + 1 = -0.224744871 u = -0.224744871 Simplifying u = -0.224744871Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.224744871, -0.224744871}
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