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Simplifying 3u2 = 30u + -6 Reorder the terms: 3u2 = -6 + 30u Solving 3u2 = -6 + 30u Solving for variable 'u'. Reorder the terms: 6 + -30u + 3u2 = -6 + 30u + 6 + -30u Reorder the terms: 6 + -30u + 3u2 = -6 + 6 + 30u + -30u Combine like terms: -6 + 6 = 0 6 + -30u + 3u2 = 0 + 30u + -30u 6 + -30u + 3u2 = 30u + -30u Combine like terms: 30u + -30u = 0 6 + -30u + 3u2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -10u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -10u + u2)' equal to zero and attempt to solve: Simplifying 2 + -10u + u2 = 0 Solving 2 + -10u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -10u + -2 + u2 = 0 + -2 Reorder the terms: 2 + -2 + -10u + u2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -10u + u2 = 0 + -2 -10u + u2 = 0 + -2 Combine like terms: 0 + -2 = -2 -10u + u2 = -2 The u term is -10u. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10u + 25 + u2 = -2 + 25 Reorder the terms: 25 + -10u + u2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + -10u + u2 = 23 Factor a perfect square on the left side: (u + -5)(u + -5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (u + -5) equal to 4.795831523 and -4.795831523.Subproblem 1
u + -5 = 4.795831523 Simplifying u + -5 = 4.795831523 Reorder the terms: -5 + u = 4.795831523 Solving -5 + u = 4.795831523 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = 4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + u = 4.795831523 + 5 u = 4.795831523 + 5 Combine like terms: 4.795831523 + 5 = 9.795831523 u = 9.795831523 Simplifying u = 9.795831523Subproblem 2
u + -5 = -4.795831523 Simplifying u + -5 = -4.795831523 Reorder the terms: -5 + u = -4.795831523 Solving -5 + u = -4.795831523 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = -4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + u = -4.795831523 + 5 u = -4.795831523 + 5 Combine like terms: -4.795831523 + 5 = 0.204168477 u = 0.204168477 Simplifying u = 0.204168477Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.795831523, 0.204168477}Solution
u = {9.795831523, 0.204168477}
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