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Simplifying 2u2 + 17u + 23 = 0 Reorder the terms: 23 + 17u + 2u2 = 0 Solving 23 + 17u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + 8.5u + u2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + 8.5u + -11.5 + u2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + 8.5u + u2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + 8.5u + u2 = 0 + -11.5 8.5u + u2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 8.5u + u2 = -11.5 The u term is 8.5u. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5u + 18.0625 + u2 = -11.5 + 18.0625 Reorder the terms: 18.0625 + 8.5u + u2 = -11.5 + 18.0625 Combine like terms: -11.5 + 18.0625 = 6.5625 18.0625 + 8.5u + u2 = 6.5625 Factor a perfect square on the left side: (u + 4.25)(u + 4.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (u + 4.25) equal to 2.561737691 and -2.561737691.Subproblem 1
u + 4.25 = 2.561737691 Simplifying u + 4.25 = 2.561737691 Reorder the terms: 4.25 + u = 2.561737691 Solving 4.25 + u = 2.561737691 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + u = 2.561737691 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + u = 2.561737691 + -4.25 u = 2.561737691 + -4.25 Combine like terms: 2.561737691 + -4.25 = -1.688262309 u = -1.688262309 Simplifying u = -1.688262309Subproblem 2
u + 4.25 = -2.561737691 Simplifying u + 4.25 = -2.561737691 Reorder the terms: 4.25 + u = -2.561737691 Solving 4.25 + u = -2.561737691 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + u = -2.561737691 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + u = -2.561737691 + -4.25 u = -2.561737691 + -4.25 Combine like terms: -2.561737691 + -4.25 = -6.811737691 u = -6.811737691 Simplifying u = -6.811737691Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.688262309, -6.811737691}
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