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Simplifying 8u2 + -48u + -6 = 0 Reorder the terms: -6 + -48u + 8u2 = 0 Solving -6 + -48u + 8u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -24u + 4u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -24u + 4u2)' equal to zero and attempt to solve: Simplifying -3 + -24u + 4u2 = 0 Solving -3 + -24u + 4u2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -6u + u2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -6u + 0.75 + u2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -6u + u2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -6u + u2 = 0 + 0.75 -6u + u2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -6u + u2 = 0.75 The u term is -6u. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6u + 9 + u2 = 0.75 + 9 Reorder the terms: 9 + -6u + u2 = 0.75 + 9 Combine like terms: 0.75 + 9 = 9.75 9 + -6u + u2 = 9.75 Factor a perfect square on the left side: (u + -3)(u + -3) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (u + -3) equal to 3.122498999 and -3.122498999.Subproblem 1
u + -3 = 3.122498999 Simplifying u + -3 = 3.122498999 Reorder the terms: -3 + u = 3.122498999 Solving -3 + u = 3.122498999 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 3.122498999 + 3 Combine like terms: -3 + 3 = 0 0 + u = 3.122498999 + 3 u = 3.122498999 + 3 Combine like terms: 3.122498999 + 3 = 6.122498999 u = 6.122498999 Simplifying u = 6.122498999Subproblem 2
u + -3 = -3.122498999 Simplifying u + -3 = -3.122498999 Reorder the terms: -3 + u = -3.122498999 Solving -3 + u = -3.122498999 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = -3.122498999 + 3 Combine like terms: -3 + 3 = 0 0 + u = -3.122498999 + 3 u = -3.122498999 + 3 Combine like terms: -3.122498999 + 3 = -0.122498999 u = -0.122498999 Simplifying u = -0.122498999Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.122498999, -0.122498999}Solution
u = {6.122498999, -0.122498999}
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