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Simplifying 4u2 + 120u = 68 Reorder the terms: 120u + 4u2 = 68 Solving 120u + 4u2 = 68 Solving for variable 'u'. Reorder the terms: -68 + 120u + 4u2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + 120u + 4u2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-17 + 30u + u2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + 30u + u2)' equal to zero and attempt to solve: Simplifying -17 + 30u + u2 = 0 Solving -17 + 30u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 30u + 17 + u2 = 0 + 17 Reorder the terms: -17 + 17 + 30u + u2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 30u + u2 = 0 + 17 30u + u2 = 0 + 17 Combine like terms: 0 + 17 = 17 30u + u2 = 17 The u term is 30u. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30u + 225 + u2 = 17 + 225 Reorder the terms: 225 + 30u + u2 = 17 + 225 Combine like terms: 17 + 225 = 242 225 + 30u + u2 = 242 Factor a perfect square on the left side: (u + 15)(u + 15) = 242 Calculate the square root of the right side: 15.556349186 Break this problem into two subproblems by setting (u + 15) equal to 15.556349186 and -15.556349186.Subproblem 1
u + 15 = 15.556349186 Simplifying u + 15 = 15.556349186 Reorder the terms: 15 + u = 15.556349186 Solving 15 + u = 15.556349186 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + u = 15.556349186 + -15 Combine like terms: 15 + -15 = 0 0 + u = 15.556349186 + -15 u = 15.556349186 + -15 Combine like terms: 15.556349186 + -15 = 0.556349186 u = 0.556349186 Simplifying u = 0.556349186Subproblem 2
u + 15 = -15.556349186 Simplifying u + 15 = -15.556349186 Reorder the terms: 15 + u = -15.556349186 Solving 15 + u = -15.556349186 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + u = -15.556349186 + -15 Combine like terms: 15 + -15 = 0 0 + u = -15.556349186 + -15 u = -15.556349186 + -15 Combine like terms: -15.556349186 + -15 = -30.556349186 u = -30.556349186 Simplifying u = -30.556349186Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.556349186, -30.556349186}Solution
u = {0.556349186, -30.556349186}
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