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Simplifying 3u2 = 30u + -12 Reorder the terms: 3u2 = -12 + 30u Solving 3u2 = -12 + 30u Solving for variable 'u'. Reorder the terms: 12 + -30u + 3u2 = -12 + 30u + 12 + -30u Reorder the terms: 12 + -30u + 3u2 = -12 + 12 + 30u + -30u Combine like terms: -12 + 12 = 0 12 + -30u + 3u2 = 0 + 30u + -30u 12 + -30u + 3u2 = 30u + -30u Combine like terms: 30u + -30u = 0 12 + -30u + 3u2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -10u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -10u + u2)' equal to zero and attempt to solve: Simplifying 4 + -10u + u2 = 0 Solving 4 + -10u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10u + -4 + u2 = 0 + -4 Reorder the terms: 4 + -4 + -10u + u2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10u + u2 = 0 + -4 -10u + u2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10u + u2 = -4 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 = -4 + 25 Reorder the terms: 25 + -10u + u2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + -10u + u2 = 21 Factor a perfect square on the left side: (u + -5)(u + -5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (u + -5) equal to 4.582575695 and -4.582575695.Subproblem 1
u + -5 = 4.582575695 Simplifying u + -5 = 4.582575695 Reorder the terms: -5 + u = 4.582575695 Solving -5 + u = 4.582575695 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 = 4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + u = 4.582575695 + 5 u = 4.582575695 + 5 Combine like terms: 4.582575695 + 5 = 9.582575695 u = 9.582575695 Simplifying u = 9.582575695Subproblem 2
u + -5 = -4.582575695 Simplifying u + -5 = -4.582575695 Reorder the terms: -5 + u = -4.582575695 Solving -5 + u = -4.582575695 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 = -4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + u = -4.582575695 + 5 u = -4.582575695 + 5 Combine like terms: -4.582575695 + 5 = 0.417424305 u = 0.417424305 Simplifying u = 0.417424305Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.582575695, 0.417424305}Solution
u = {9.582575695, 0.417424305}
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