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Simplifying -2u(2u + -5) + 6u = -4(u + 1) Reorder the terms: -2u(-5 + 2u) + 6u = -4(u + 1) (-5 * -2u + 2u * -2u) + 6u = -4(u + 1) (10u + -4u2) + 6u = -4(u + 1) Reorder the terms: 10u + 6u + -4u2 = -4(u + 1) Combine like terms: 10u + 6u = 16u 16u + -4u2 = -4(u + 1) Reorder the terms: 16u + -4u2 = -4(1 + u) 16u + -4u2 = (1 * -4 + u * -4) 16u + -4u2 = (-4 + -4u) Solving 16u + -4u2 = -4 + -4u Solving for variable 'u'. Reorder the terms: 4 + 16u + 4u + -4u2 = -4 + -4u + 4 + 4u Combine like terms: 16u + 4u = 20u 4 + 20u + -4u2 = -4 + -4u + 4 + 4u Reorder the terms: 4 + 20u + -4u2 = -4 + 4 + -4u + 4u Combine like terms: -4 + 4 = 0 4 + 20u + -4u2 = 0 + -4u + 4u 4 + 20u + -4u2 = -4u + 4u Combine like terms: -4u + 4u = 0 4 + 20u + -4u2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 5u + -1u2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 5u + -1u2)' equal to zero and attempt to solve: Simplifying 1 + 5u + -1u2 = 0 Solving 1 + 5u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -5u + u2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + -5u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5u + u2 = 0 + 1 -5u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5u + u2 = 1 The u term is -5u. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5u + 6.25 + u2 = 1 + 6.25 Reorder the terms: 6.25 + -5u + u2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + -5u + u2 = 7.25 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (u + -2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
u + -2.5 = 2.692582404 Simplifying u + -2.5 = 2.692582404 Reorder the terms: -2.5 + u = 2.692582404 Solving -2.5 + u = 2.692582404 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + u = 2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 2.692582404 + 2.5 u = 2.692582404 + 2.5 Combine like terms: 2.692582404 + 2.5 = 5.192582404 u = 5.192582404 Simplifying u = 5.192582404Subproblem 2
u + -2.5 = -2.692582404 Simplifying u + -2.5 = -2.692582404 Reorder the terms: -2.5 + u = -2.692582404 Solving -2.5 + u = -2.692582404 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + u = -2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -2.692582404 + 2.5 u = -2.692582404 + 2.5 Combine like terms: -2.692582404 + 2.5 = -0.192582404 u = -0.192582404 Simplifying u = -0.192582404Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.192582404, -0.192582404}Solution
u = {5.192582404, -0.192582404}
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