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Simplifying 2u2 + -22u + 16 = 0 Reorder the terms: 16 + -22u + 2u2 = 0 Solving 16 + -22u + 2u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -11u + u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -11u + u2)' equal to zero and attempt to solve: Simplifying 8 + -11u + u2 = 0 Solving 8 + -11u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -11u + -8 + u2 = 0 + -8 Reorder the terms: 8 + -8 + -11u + u2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -11u + u2 = 0 + -8 -11u + u2 = 0 + -8 Combine like terms: 0 + -8 = -8 -11u + u2 = -8 The u term is -11u. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11u + 30.25 + u2 = -8 + 30.25 Reorder the terms: 30.25 + -11u + u2 = -8 + 30.25 Combine like terms: -8 + 30.25 = 22.25 30.25 + -11u + u2 = 22.25 Factor a perfect square on the left side: (u + -5.5)(u + -5.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (u + -5.5) equal to 4.716990566 and -4.716990566.Subproblem 1
u + -5.5 = 4.716990566 Simplifying u + -5.5 = 4.716990566 Reorder the terms: -5.5 + u = 4.716990566 Solving -5.5 + u = 4.716990566 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + u = 4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + u = 4.716990566 + 5.5 u = 4.716990566 + 5.5 Combine like terms: 4.716990566 + 5.5 = 10.216990566 u = 10.216990566 Simplifying u = 10.216990566Subproblem 2
u + -5.5 = -4.716990566 Simplifying u + -5.5 = -4.716990566 Reorder the terms: -5.5 + u = -4.716990566 Solving -5.5 + u = -4.716990566 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + u = -4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + u = -4.716990566 + 5.5 u = -4.716990566 + 5.5 Combine like terms: -4.716990566 + 5.5 = 0.783009434 u = 0.783009434 Simplifying u = 0.783009434Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.216990566, 0.783009434}Solution
u = {10.216990566, 0.783009434}
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