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Simplifying 8(4u + -1) + -12u = u(2u + -6) Reorder the terms: 8(-1 + 4u) + -12u = u(2u + -6) (-1 * 8 + 4u * 8) + -12u = u(2u + -6) (-8 + 32u) + -12u = u(2u + -6) Combine like terms: 32u + -12u = 20u -8 + 20u = u(2u + -6) Reorder the terms: -8 + 20u = u(-6 + 2u) -8 + 20u = (-6 * u + 2u * u) -8 + 20u = (-6u + 2u2) Solving -8 + 20u = -6u + 2u2 Solving for variable 'u'. Combine like terms: 20u + 6u = 26u -8 + 26u + -2u2 = -6u + 2u2 + 6u + -2u2 Reorder the terms: -8 + 26u + -2u2 = -6u + 6u + 2u2 + -2u2 Combine like terms: -6u + 6u = 0 -8 + 26u + -2u2 = 0 + 2u2 + -2u2 -8 + 26u + -2u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -8 + 26u + -2u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 13u + -1u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 13u + -1u2)' equal to zero and attempt to solve: Simplifying -4 + 13u + -1u2 = 0 Solving -4 + 13u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -13u + u2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -13u + -4 + u2 = 0 + -4 Reorder the terms: 4 + -4 + -13u + u2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -13u + u2 = 0 + -4 -13u + u2 = 0 + -4 Combine like terms: 0 + -4 = -4 -13u + u2 = -4 The u term is -13u. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13u + 42.25 + u2 = -4 + 42.25 Reorder the terms: 42.25 + -13u + u2 = -4 + 42.25 Combine like terms: -4 + 42.25 = 38.25 42.25 + -13u + u2 = 38.25 Factor a perfect square on the left side: (u + -6.5)(u + -6.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (u + -6.5) equal to 6.184658438 and -6.184658438.Subproblem 1
u + -6.5 = 6.184658438 Simplifying u + -6.5 = 6.184658438 Reorder the terms: -6.5 + u = 6.184658438 Solving -6.5 + u = 6.184658438 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = 6.184658438 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = 6.184658438 + 6.5 u = 6.184658438 + 6.5 Combine like terms: 6.184658438 + 6.5 = 12.684658438 u = 12.684658438 Simplifying u = 12.684658438Subproblem 2
u + -6.5 = -6.184658438 Simplifying u + -6.5 = -6.184658438 Reorder the terms: -6.5 + u = -6.184658438 Solving -6.5 + u = -6.184658438 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = -6.184658438 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = -6.184658438 + 6.5 u = -6.184658438 + 6.5 Combine like terms: -6.184658438 + 6.5 = 0.315341562 u = 0.315341562 Simplifying u = 0.315341562Solution
The solution to the problem is based on the solutions from the subproblems. u = {12.684658438, 0.315341562}Solution
u = {12.684658438, 0.315341562}
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