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Simplifying u2 + 32u + -50 = 0 Reorder the terms: -50 + 32u + u2 = 0 Solving -50 + 32u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 32u + 50 + u2 = 0 + 50 Reorder the terms: -50 + 50 + 32u + u2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 32u + u2 = 0 + 50 32u + u2 = 0 + 50 Combine like terms: 0 + 50 = 50 32u + u2 = 50 The u term is 32u. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32u + 256 + u2 = 50 + 256 Reorder the terms: 256 + 32u + u2 = 50 + 256 Combine like terms: 50 + 256 = 306 256 + 32u + u2 = 306 Factor a perfect square on the left side: (u + 16)(u + 16) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (u + 16) equal to 17.492855685 and -17.492855685.Subproblem 1
u + 16 = 17.492855685 Simplifying u + 16 = 17.492855685 Reorder the terms: 16 + u = 17.492855685 Solving 16 + u = 17.492855685 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + u = 17.492855685 + -16 Combine like terms: 16 + -16 = 0 0 + u = 17.492855685 + -16 u = 17.492855685 + -16 Combine like terms: 17.492855685 + -16 = 1.492855685 u = 1.492855685 Simplifying u = 1.492855685Subproblem 2
u + 16 = -17.492855685 Simplifying u + 16 = -17.492855685 Reorder the terms: 16 + u = -17.492855685 Solving 16 + u = -17.492855685 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + u = -17.492855685 + -16 Combine like terms: 16 + -16 = 0 0 + u = -17.492855685 + -16 u = -17.492855685 + -16 Combine like terms: -17.492855685 + -16 = -33.492855685 u = -33.492855685 Simplifying u = -33.492855685Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.492855685, -33.492855685}
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