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Simplifying -1u = 2u2 + -49 Reorder the terms: -1u = -49 + 2u2 Solving -1u = -49 + 2u2 Solving for variable 'u'. Reorder the terms: 49 + -1u + -2u2 = -49 + 2u2 + 49 + -2u2 Reorder the terms: 49 + -1u + -2u2 = -49 + 49 + 2u2 + -2u2 Combine like terms: -49 + 49 = 0 49 + -1u + -2u2 = 0 + 2u2 + -2u2 49 + -1u + -2u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 49 + -1u + -2u2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -24.5 + 0.5u + u2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + 0.5u + 24.5 + u2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + 0.5u + u2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + 0.5u + u2 = 0 + 24.5 0.5u + u2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 0.5u + u2 = 24.5 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 = 24.5 + 0.0625 Reorder the terms: 0.0625 + 0.5u + u2 = 24.5 + 0.0625 Combine like terms: 24.5 + 0.0625 = 24.5625 0.0625 + 0.5u + u2 = 24.5625 Factor a perfect square on the left side: (u + 0.25)(u + 0.25) = 24.5625 Calculate the square root of the right side: 4.9560569 Break this problem into two subproblems by setting (u + 0.25) equal to 4.9560569 and -4.9560569.Subproblem 1
u + 0.25 = 4.9560569 Simplifying u + 0.25 = 4.9560569 Reorder the terms: 0.25 + u = 4.9560569 Solving 0.25 + u = 4.9560569 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 = 4.9560569 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + u = 4.9560569 + -0.25 u = 4.9560569 + -0.25 Combine like terms: 4.9560569 + -0.25 = 4.7060569 u = 4.7060569 Simplifying u = 4.7060569Subproblem 2
u + 0.25 = -4.9560569 Simplifying u + 0.25 = -4.9560569 Reorder the terms: 0.25 + u = -4.9560569 Solving 0.25 + u = -4.9560569 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 = -4.9560569 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + u = -4.9560569 + -0.25 u = -4.9560569 + -0.25 Combine like terms: -4.9560569 + -0.25 = -5.2060569 u = -5.2060569 Simplifying u = -5.2060569Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.7060569, -5.2060569}
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