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Simplifying 4u + -5 + 3(2u + 1) = -2u(u + 4) Reorder the terms: 4u + -5 + 3(1 + 2u) = -2u(u + 4) 4u + -5 + (1 * 3 + 2u * 3) = -2u(u + 4) 4u + -5 + (3 + 6u) = -2u(u + 4) Reorder the terms: -5 + 3 + 4u + 6u = -2u(u + 4) Combine like terms: -5 + 3 = -2 -2 + 4u + 6u = -2u(u + 4) Combine like terms: 4u + 6u = 10u -2 + 10u = -2u(u + 4) Reorder the terms: -2 + 10u = -2u(4 + u) -2 + 10u = (4 * -2u + u * -2u) -2 + 10u = (-8u + -2u2) Solving -2 + 10u = -8u + -2u2 Solving for variable 'u'. Combine like terms: 10u + 8u = 18u -2 + 18u + 2u2 = -8u + -2u2 + 8u + 2u2 Reorder the terms: -2 + 18u + 2u2 = -8u + 8u + -2u2 + 2u2 Combine like terms: -8u + 8u = 0 -2 + 18u + 2u2 = 0 + -2u2 + 2u2 -2 + 18u + 2u2 = -2u2 + 2u2 Combine like terms: -2u2 + 2u2 = 0 -2 + 18u + 2u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 9u + u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 9u + u2)' equal to zero and attempt to solve: Simplifying -1 + 9u + u2 = 0 Solving -1 + 9u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 9u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + 9u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 9u + u2 = 0 + 1 9u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 9u + u2 = 1 The u term is 9u. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9u + 20.25 + u2 = 1 + 20.25 Reorder the terms: 20.25 + 9u + u2 = 1 + 20.25 Combine like terms: 1 + 20.25 = 21.25 20.25 + 9u + u2 = 21.25 Factor a perfect square on the left side: (u + 4.5)(u + 4.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (u + 4.5) equal to 4.609772229 and -4.609772229.Subproblem 1
u + 4.5 = 4.609772229 Simplifying u + 4.5 = 4.609772229 Reorder the terms: 4.5 + u = 4.609772229 Solving 4.5 + u = 4.609772229 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = 4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = 4.609772229 + -4.5 u = 4.609772229 + -4.5 Combine like terms: 4.609772229 + -4.5 = 0.109772229 u = 0.109772229 Simplifying u = 0.109772229Subproblem 2
u + 4.5 = -4.609772229 Simplifying u + 4.5 = -4.609772229 Reorder the terms: 4.5 + u = -4.609772229 Solving 4.5 + u = -4.609772229 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = -4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = -4.609772229 + -4.5 u = -4.609772229 + -4.5 Combine like terms: -4.609772229 + -4.5 = -9.109772229 u = -9.109772229 Simplifying u = -9.109772229Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.109772229, -9.109772229}Solution
u = {0.109772229, -9.109772229}
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