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Simplifying 4u2 + -64u + 178 = 0 Reorder the terms: 178 + -64u + 4u2 = 0 Solving 178 + -64u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(89 + -32u + 2u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(89 + -32u + 2u2)' equal to zero and attempt to solve: Simplifying 89 + -32u + 2u2 = 0 Solving 89 + -32u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 44.5 + -16u + u2 = 0 Move the constant term to the right: Add '-44.5' to each side of the equation. 44.5 + -16u + -44.5 + u2 = 0 + -44.5 Reorder the terms: 44.5 + -44.5 + -16u + u2 = 0 + -44.5 Combine like terms: 44.5 + -44.5 = 0.0 0.0 + -16u + u2 = 0 + -44.5 -16u + u2 = 0 + -44.5 Combine like terms: 0 + -44.5 = -44.5 -16u + u2 = -44.5 The u term is -16u. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16u + 64 + u2 = -44.5 + 64 Reorder the terms: 64 + -16u + u2 = -44.5 + 64 Combine like terms: -44.5 + 64 = 19.5 64 + -16u + u2 = 19.5 Factor a perfect square on the left side: (u + -8)(u + -8) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (u + -8) equal to 4.415880433 and -4.415880433.Subproblem 1
u + -8 = 4.415880433 Simplifying u + -8 = 4.415880433 Reorder the terms: -8 + u = 4.415880433 Solving -8 + u = 4.415880433 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + u = 4.415880433 + 8 Combine like terms: -8 + 8 = 0 0 + u = 4.415880433 + 8 u = 4.415880433 + 8 Combine like terms: 4.415880433 + 8 = 12.415880433 u = 12.415880433 Simplifying u = 12.415880433Subproblem 2
u + -8 = -4.415880433 Simplifying u + -8 = -4.415880433 Reorder the terms: -8 + u = -4.415880433 Solving -8 + u = -4.415880433 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + u = -4.415880433 + 8 Combine like terms: -8 + 8 = 0 0 + u = -4.415880433 + 8 u = -4.415880433 + 8 Combine like terms: -4.415880433 + 8 = 3.584119567 u = 3.584119567 Simplifying u = 3.584119567Solution
The solution to the problem is based on the solutions from the subproblems. u = {12.415880433, 3.584119567}Solution
u = {12.415880433, 3.584119567}
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