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Simplifying 36u2 + 160u + 128 = 0 Reorder the terms: 128 + 160u + 36u2 = 0 Solving 128 + 160u + 36u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '4'. 4(32 + 40u + 9u2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(32 + 40u + 9u2)' equal to zero and attempt to solve: Simplifying 32 + 40u + 9u2 = 0 Solving 32 + 40u + 9u2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 3.555555556 + 4.444444444u + u2 = 0 Move the constant term to the right: Add '-3.555555556' to each side of the equation. 3.555555556 + 4.444444444u + -3.555555556 + u2 = 0 + -3.555555556 Reorder the terms: 3.555555556 + -3.555555556 + 4.444444444u + u2 = 0 + -3.555555556 Combine like terms: 3.555555556 + -3.555555556 = 0.000000000 0.000000000 + 4.444444444u + u2 = 0 + -3.555555556 4.444444444u + u2 = 0 + -3.555555556 Combine like terms: 0 + -3.555555556 = -3.555555556 4.444444444u + u2 = -3.555555556 The u term is 4.444444444u. Take half its coefficient (2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. 4.444444444u + 4.938271604 + u2 = -3.555555556 + 4.938271604 Reorder the terms: 4.938271604 + 4.444444444u + u2 = -3.555555556 + 4.938271604 Combine like terms: -3.555555556 + 4.938271604 = 1.382716048 4.938271604 + 4.444444444u + u2 = 1.382716048 Factor a perfect square on the left side: (u + 2.222222222)(u + 2.222222222) = 1.382716048 Calculate the square root of the right side: 1.175889471 Break this problem into two subproblems by setting (u + 2.222222222) equal to 1.175889471 and -1.175889471.Subproblem 1
u + 2.222222222 = 1.175889471 Simplifying u + 2.222222222 = 1.175889471 Reorder the terms: 2.222222222 + u = 1.175889471 Solving 2.222222222 + u = 1.175889471 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.222222222' to each side of the equation. 2.222222222 + -2.222222222 + u = 1.175889471 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + u = 1.175889471 + -2.222222222 u = 1.175889471 + -2.222222222 Combine like terms: 1.175889471 + -2.222222222 = -1.046332751 u = -1.046332751 Simplifying u = -1.046332751Subproblem 2
u + 2.222222222 = -1.175889471 Simplifying u + 2.222222222 = -1.175889471 Reorder the terms: 2.222222222 + u = -1.175889471 Solving 2.222222222 + u = -1.175889471 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.222222222' to each side of the equation. 2.222222222 + -2.222222222 + u = -1.175889471 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + u = -1.175889471 + -2.222222222 u = -1.175889471 + -2.222222222 Combine like terms: -1.175889471 + -2.222222222 = -3.398111693 u = -3.398111693 Simplifying u = -3.398111693Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.046332751, -3.398111693}Solution
u = {-1.046332751, -3.398111693}
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