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Simplifying 3u2 = 30u + -9 Reorder the terms: 3u2 = -9 + 30u Solving 3u2 = -9 + 30u Solving for variable 'u'. Reorder the terms: 9 + -30u + 3u2 = -9 + 30u + 9 + -30u Reorder the terms: 9 + -30u + 3u2 = -9 + 9 + 30u + -30u Combine like terms: -9 + 9 = 0 9 + -30u + 3u2 = 0 + 30u + -30u 9 + -30u + 3u2 = 30u + -30u Combine like terms: 30u + -30u = 0 9 + -30u + 3u2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -10u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -10u + u2)' equal to zero and attempt to solve: Simplifying 3 + -10u + u2 = 0 Solving 3 + -10u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -10u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10u + u2 = 0 + -3 -10u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10u + u2 = -3 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 = -3 + 25 Reorder the terms: 25 + -10u + u2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + -10u + u2 = 22 Factor a perfect square on the left side: (u + -5)(u + -5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (u + -5) equal to 4.69041576 and -4.69041576.Subproblem 1
u + -5 = 4.69041576 Simplifying u + -5 = 4.69041576 Reorder the terms: -5 + u = 4.69041576 Solving -5 + u = 4.69041576 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 = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + u = 4.69041576 + 5 u = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 u = 9.69041576 Simplifying u = 9.69041576Subproblem 2
u + -5 = -4.69041576 Simplifying u + -5 = -4.69041576 Reorder the terms: -5 + u = -4.69041576 Solving -5 + u = -4.69041576 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 = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + u = -4.69041576 + 5 u = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 u = 0.30958424 Simplifying u = 0.30958424Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.69041576, 0.30958424}Solution
u = {9.69041576, 0.30958424}
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