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Simplifying 2u2 + 13u + 24 = u2 + 36 Reorder the terms: 24 + 13u + 2u2 = u2 + 36 Reorder the terms: 24 + 13u + 2u2 = 36 + u2 Solving 24 + 13u + 2u2 = 36 + u2 Solving for variable 'u'. Reorder the terms: 24 + -36 + 13u + 2u2 + -1u2 = 36 + u2 + -36 + -1u2 Combine like terms: 24 + -36 = -12 -12 + 13u + 2u2 + -1u2 = 36 + u2 + -36 + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 -12 + 13u + 1u2 = 36 + u2 + -36 + -1u2 Reorder the terms: -12 + 13u + 1u2 = 36 + -36 + u2 + -1u2 Combine like terms: 36 + -36 = 0 -12 + 13u + 1u2 = 0 + u2 + -1u2 -12 + 13u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -12 + 13u + 1u2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 13u + 12 + u2 = 0 + 12 Reorder the terms: -12 + 12 + 13u + u2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 13u + u2 = 0 + 12 13u + u2 = 0 + 12 Combine like terms: 0 + 12 = 12 13u + u2 = 12 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 = 12 + 42.25 Reorder the terms: 42.25 + 13u + u2 = 12 + 42.25 Combine like terms: 12 + 42.25 = 54.25 42.25 + 13u + u2 = 54.25 Factor a perfect square on the left side: (u + 6.5)(u + 6.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (u + 6.5) equal to 7.365459931 and -7.365459931.Subproblem 1
u + 6.5 = 7.365459931 Simplifying u + 6.5 = 7.365459931 Reorder the terms: 6.5 + u = 7.365459931 Solving 6.5 + u = 7.365459931 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 = 7.365459931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + u = 7.365459931 + -6.5 u = 7.365459931 + -6.5 Combine like terms: 7.365459931 + -6.5 = 0.865459931 u = 0.865459931 Simplifying u = 0.865459931Subproblem 2
u + 6.5 = -7.365459931 Simplifying u + 6.5 = -7.365459931 Reorder the terms: 6.5 + u = -7.365459931 Solving 6.5 + u = -7.365459931 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 = -7.365459931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + u = -7.365459931 + -6.5 u = -7.365459931 + -6.5 Combine like terms: -7.365459931 + -6.5 = -13.865459931 u = -13.865459931 Simplifying u = -13.865459931Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.865459931, -13.865459931}
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