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Simplifying 2u2 + -12u = 58 Reorder the terms: -12u + 2u2 = 58 Solving -12u + 2u2 = 58 Solving for variable 'u'. Reorder the terms: -58 + -12u + 2u2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + -12u + 2u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -6u + u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -6u + u2)' equal to zero and attempt to solve: Simplifying -29 + -6u + u2 = 0 Solving -29 + -6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -6u + 29 + u2 = 0 + 29 Reorder the terms: -29 + 29 + -6u + u2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -6u + u2 = 0 + 29 -6u + u2 = 0 + 29 Combine like terms: 0 + 29 = 29 -6u + u2 = 29 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 = 29 + 9 Reorder the terms: 9 + -6u + u2 = 29 + 9 Combine like terms: 29 + 9 = 38 9 + -6u + u2 = 38 Factor a perfect square on the left side: (u + -3)(u + -3) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (u + -3) equal to 6.164414003 and -6.164414003.Subproblem 1
u + -3 = 6.164414003 Simplifying u + -3 = 6.164414003 Reorder the terms: -3 + u = 6.164414003 Solving -3 + u = 6.164414003 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 = 6.164414003 + 3 Combine like terms: -3 + 3 = 0 0 + u = 6.164414003 + 3 u = 6.164414003 + 3 Combine like terms: 6.164414003 + 3 = 9.164414003 u = 9.164414003 Simplifying u = 9.164414003Subproblem 2
u + -3 = -6.164414003 Simplifying u + -3 = -6.164414003 Reorder the terms: -3 + u = -6.164414003 Solving -3 + u = -6.164414003 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 = -6.164414003 + 3 Combine like terms: -3 + 3 = 0 0 + u = -6.164414003 + 3 u = -6.164414003 + 3 Combine like terms: -6.164414003 + 3 = -3.164414003 u = -3.164414003 Simplifying u = -3.164414003Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.164414003, -3.164414003}Solution
u = {9.164414003, -3.164414003}
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