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Simplifying 6u2 + 60u = 96 Reorder the terms: 60u + 6u2 = 96 Solving 60u + 6u2 = 96 Solving for variable 'u'. Reorder the terms: -96 + 60u + 6u2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 60u + 6u2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-16 + 10u + u2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-16 + 10u + u2)' equal to zero and attempt to solve: Simplifying -16 + 10u + u2 = 0 Solving -16 + 10u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 10u + 16 + u2 = 0 + 16 Reorder the terms: -16 + 16 + 10u + u2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 10u + u2 = 0 + 16 10u + u2 = 0 + 16 Combine like terms: 0 + 16 = 16 10u + u2 = 16 The u term is 10u. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10u + 25 + u2 = 16 + 25 Reorder the terms: 25 + 10u + u2 = 16 + 25 Combine like terms: 16 + 25 = 41 25 + 10u + u2 = 41 Factor a perfect square on the left side: (u + 5)(u + 5) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (u + 5) equal to 6.403124237 and -6.403124237.Subproblem 1
u + 5 = 6.403124237 Simplifying u + 5 = 6.403124237 Reorder the terms: 5 + u = 6.403124237 Solving 5 + u = 6.403124237 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = 6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + u = 6.403124237 + -5 u = 6.403124237 + -5 Combine like terms: 6.403124237 + -5 = 1.403124237 u = 1.403124237 Simplifying u = 1.403124237Subproblem 2
u + 5 = -6.403124237 Simplifying u + 5 = -6.403124237 Reorder the terms: 5 + u = -6.403124237 Solving 5 + u = -6.403124237 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = -6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + u = -6.403124237 + -5 u = -6.403124237 + -5 Combine like terms: -6.403124237 + -5 = -11.403124237 u = -11.403124237 Simplifying u = -11.403124237Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.403124237, -11.403124237}Solution
u = {1.403124237, -11.403124237}
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