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Simplifying 2u2 + -19u + 35 = 9 Reorder the terms: 35 + -19u + 2u2 = 9 Solving 35 + -19u + 2u2 = 9 Solving for variable 'u'. Reorder the terms: 35 + -9 + -19u + 2u2 = 9 + -9 Combine like terms: 35 + -9 = 26 26 + -19u + 2u2 = 9 + -9 Combine like terms: 9 + -9 = 0 26 + -19u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13 + -9.5u + u2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -9.5u + -13 + u2 = 0 + -13 Reorder the terms: 13 + -13 + -9.5u + u2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -9.5u + u2 = 0 + -13 -9.5u + u2 = 0 + -13 Combine like terms: 0 + -13 = -13 -9.5u + u2 = -13 The u term is -9.5u. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5u + 22.5625 + u2 = -13 + 22.5625 Reorder the terms: 22.5625 + -9.5u + u2 = -13 + 22.5625 Combine like terms: -13 + 22.5625 = 9.5625 22.5625 + -9.5u + u2 = 9.5625 Factor a perfect square on the left side: (u + -4.75)(u + -4.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (u + -4.75) equal to 3.092329219 and -3.092329219.Subproblem 1
u + -4.75 = 3.092329219 Simplifying u + -4.75 = 3.092329219 Reorder the terms: -4.75 + u = 3.092329219 Solving -4.75 + u = 3.092329219 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + u = 3.092329219 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + u = 3.092329219 + 4.75 u = 3.092329219 + 4.75 Combine like terms: 3.092329219 + 4.75 = 7.842329219 u = 7.842329219 Simplifying u = 7.842329219Subproblem 2
u + -4.75 = -3.092329219 Simplifying u + -4.75 = -3.092329219 Reorder the terms: -4.75 + u = -3.092329219 Solving -4.75 + u = -3.092329219 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + u = -3.092329219 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + u = -3.092329219 + 4.75 u = -3.092329219 + 4.75 Combine like terms: -3.092329219 + 4.75 = 1.657670781 u = 1.657670781 Simplifying u = 1.657670781Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.842329219, 1.657670781}
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