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Simplifying 2u2 + 16u + 34 + -1u2 + 10u + 25 = 0 Reorder the terms: 34 + 25 + 16u + 10u + 2u2 + -1u2 = 0 Combine like terms: 34 + 25 = 59 59 + 16u + 10u + 2u2 + -1u2 = 0 Combine like terms: 16u + 10u = 26u 59 + 26u + 2u2 + -1u2 = 0 Combine like terms: 2u2 + -1u2 = 1u2 59 + 26u + 1u2 = 0 Solving 59 + 26u + 1u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 26u + -59 + u2 = 0 + -59 Reorder the terms: 59 + -59 + 26u + u2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 26u + u2 = 0 + -59 26u + u2 = 0 + -59 Combine like terms: 0 + -59 = -59 26u + u2 = -59 The u term is 26u. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26u + 169 + u2 = -59 + 169 Reorder the terms: 169 + 26u + u2 = -59 + 169 Combine like terms: -59 + 169 = 110 169 + 26u + u2 = 110 Factor a perfect square on the left side: (u + 13)(u + 13) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (u + 13) equal to 10.488088482 and -10.488088482.Subproblem 1
u + 13 = 10.488088482 Simplifying u + 13 = 10.488088482 Reorder the terms: 13 + u = 10.488088482 Solving 13 + u = 10.488088482 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + u = 10.488088482 + -13 Combine like terms: 13 + -13 = 0 0 + u = 10.488088482 + -13 u = 10.488088482 + -13 Combine like terms: 10.488088482 + -13 = -2.511911518 u = -2.511911518 Simplifying u = -2.511911518Subproblem 2
u + 13 = -10.488088482 Simplifying u + 13 = -10.488088482 Reorder the terms: 13 + u = -10.488088482 Solving 13 + u = -10.488088482 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + u = -10.488088482 + -13 Combine like terms: 13 + -13 = 0 0 + u = -10.488088482 + -13 u = -10.488088482 + -13 Combine like terms: -10.488088482 + -13 = -23.488088482 u = -23.488088482 Simplifying u = -23.488088482Solution
The solution to the problem is based on the solutions from the subproblems. u = {-2.511911518, -23.488088482}
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