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Simplifying 0 = -4u2 + -31u + -50 Reorder the terms: 0 = -50 + -31u + -4u2 Solving 0 = -50 + -31u + -4u2 Solving for variable 'u'. Combine like terms: 0 + 50 = 50 50 + 31u + 4u2 = -50 + -31u + -4u2 + 50 + 31u + 4u2 Reorder the terms: 50 + 31u + 4u2 = -50 + 50 + -31u + 31u + -4u2 + 4u2 Combine like terms: -50 + 50 = 0 50 + 31u + 4u2 = 0 + -31u + 31u + -4u2 + 4u2 50 + 31u + 4u2 = -31u + 31u + -4u2 + 4u2 Combine like terms: -31u + 31u = 0 50 + 31u + 4u2 = 0 + -4u2 + 4u2 50 + 31u + 4u2 = -4u2 + 4u2 Combine like terms: -4u2 + 4u2 = 0 50 + 31u + 4u2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.5 + 7.75u + u2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 7.75u + -12.5 + u2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 7.75u + u2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 7.75u + u2 = 0 + -12.5 7.75u + u2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 7.75u + u2 = -12.5 The u term is 7.75u. Take half its coefficient (3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. 7.75u + 15.015625 + u2 = -12.5 + 15.015625 Reorder the terms: 15.015625 + 7.75u + u2 = -12.5 + 15.015625 Combine like terms: -12.5 + 15.015625 = 2.515625 15.015625 + 7.75u + u2 = 2.515625 Factor a perfect square on the left side: (u + 3.875)(u + 3.875) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (u + 3.875) equal to 1.586072193 and -1.586072193.Subproblem 1
u + 3.875 = 1.586072193 Simplifying u + 3.875 = 1.586072193 Reorder the terms: 3.875 + u = 1.586072193 Solving 3.875 + u = 1.586072193 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + u = 1.586072193 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + u = 1.586072193 + -3.875 u = 1.586072193 + -3.875 Combine like terms: 1.586072193 + -3.875 = -2.288927807 u = -2.288927807 Simplifying u = -2.288927807Subproblem 2
u + 3.875 = -1.586072193 Simplifying u + 3.875 = -1.586072193 Reorder the terms: 3.875 + u = -1.586072193 Solving 3.875 + u = -1.586072193 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + u = -1.586072193 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + u = -1.586072193 + -3.875 u = -1.586072193 + -3.875 Combine like terms: -1.586072193 + -3.875 = -5.461072193 u = -5.461072193 Simplifying u = -5.461072193Solution
The solution to the problem is based on the solutions from the subproblems. u = {-2.288927807, -5.461072193}
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