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Simplifying (2u2) + -13u + 7 = (u2) + -25 Reorder the terms: 7 + -13u + (2u2) = (u2) + -25 7 + -13u + (2u2) = u2 + -25 Reorder the terms: 7 + -13u + (2u2) = -25 + u2 Solving 7 + -13u + (2u2) = -25 + u2 Solving for variable 'u'. Reorder the terms: 7 + 25 + -13u + (2u2) + -1u2 = -25 + u2 + 25 + -1u2 Combine like terms: 7 + 25 = 32 32 + -13u + (2u2) + -1u2 = -25 + u2 + 25 + -1u2 Combine like terms: (2u2) + -1u2 = 1u2 32 + -13u + 1u2 = -25 + u2 + 25 + -1u2 Reorder the terms: 32 + -13u + 1u2 = -25 + 25 + u2 + -1u2 Combine like terms: -25 + 25 = 0 32 + -13u + 1u2 = 0 + u2 + -1u2 32 + -13u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 32 + -13u + 1u2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -13u + -32 + u2 = 0 + -32 Reorder the terms: 32 + -32 + -13u + u2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -13u + u2 = 0 + -32 -13u + u2 = 0 + -32 Combine like terms: 0 + -32 = -32 -13u + u2 = -32 The u term is -13u. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13u + 42.25 + u2 = -32 + 42.25 Reorder the terms: 42.25 + -13u + u2 = -32 + 42.25 Combine like terms: -32 + 42.25 = 10.25 42.25 + -13u + u2 = 10.25 Factor a perfect square on the left side: (u + -6.5)(u + -6.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (u + -6.5) equal to 3.201562119 and -3.201562119.Subproblem 1
u + -6.5 = 3.201562119 Simplifying u + -6.5 = 3.201562119 Reorder the terms: -6.5 + u = 3.201562119 Solving -6.5 + u = 3.201562119 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = 3.201562119 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = 3.201562119 + 6.5 u = 3.201562119 + 6.5 Combine like terms: 3.201562119 + 6.5 = 9.701562119 u = 9.701562119 Simplifying u = 9.701562119Subproblem 2
u + -6.5 = -3.201562119 Simplifying u + -6.5 = -3.201562119 Reorder the terms: -6.5 + u = -3.201562119 Solving -6.5 + u = -3.201562119 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = -3.201562119 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = -3.201562119 + 6.5 u = -3.201562119 + 6.5 Combine like terms: -3.201562119 + 6.5 = 3.298437881 u = 3.298437881 Simplifying u = 3.298437881Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.701562119, 3.298437881}
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