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Simplifying u2 + 13u + 10 = 0 Reorder the terms: 10 + 13u + u2 = 0 Solving 10 + 13u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 13u + -10 + u2 = 0 + -10 Reorder the terms: 10 + -10 + 13u + u2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 13u + u2 = 0 + -10 13u + u2 = 0 + -10 Combine like terms: 0 + -10 = -10 13u + u2 = -10 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 = -10 + 42.25 Reorder the terms: 42.25 + 13u + u2 = -10 + 42.25 Combine like terms: -10 + 42.25 = 32.25 42.25 + 13u + u2 = 32.25 Factor a perfect square on the left side: (u + 6.5)(u + 6.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (u + 6.5) equal to 5.678908346 and -5.678908346.Subproblem 1
u + 6.5 = 5.678908346 Simplifying u + 6.5 = 5.678908346 Reorder the terms: 6.5 + u = 5.678908346 Solving 6.5 + u = 5.678908346 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 = 5.678908346 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + u = 5.678908346 + -6.5 u = 5.678908346 + -6.5 Combine like terms: 5.678908346 + -6.5 = -0.821091654 u = -0.821091654 Simplifying u = -0.821091654Subproblem 2
u + 6.5 = -5.678908346 Simplifying u + 6.5 = -5.678908346 Reorder the terms: 6.5 + u = -5.678908346 Solving 6.5 + u = -5.678908346 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 = -5.678908346 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + u = -5.678908346 + -6.5 u = -5.678908346 + -6.5 Combine like terms: -5.678908346 + -6.5 = -12.178908346 u = -12.178908346 Simplifying u = -12.178908346Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.821091654, -12.178908346}
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