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Simplifying -3u2 + -48u = 51 Reorder the terms: -48u + -3u2 = 51 Solving -48u + -3u2 = 51 Solving for variable 'u'. Reorder the terms: -51 + -48u + -3u2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + -48u + -3u2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(17 + 16u + u2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(17 + 16u + u2)' equal to zero and attempt to solve: Simplifying 17 + 16u + u2 = 0 Solving 17 + 16u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 16u + -17 + u2 = 0 + -17 Reorder the terms: 17 + -17 + 16u + u2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 16u + u2 = 0 + -17 16u + u2 = 0 + -17 Combine like terms: 0 + -17 = -17 16u + u2 = -17 The u term is 16u. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16u + 64 + u2 = -17 + 64 Reorder the terms: 64 + 16u + u2 = -17 + 64 Combine like terms: -17 + 64 = 47 64 + 16u + u2 = 47 Factor a perfect square on the left side: (u + 8)(u + 8) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (u + 8) equal to 6.8556546 and -6.8556546.Subproblem 1
u + 8 = 6.8556546 Simplifying u + 8 = 6.8556546 Reorder the terms: 8 + u = 6.8556546 Solving 8 + u = 6.8556546 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = 6.8556546 + -8 Combine like terms: 8 + -8 = 0 0 + u = 6.8556546 + -8 u = 6.8556546 + -8 Combine like terms: 6.8556546 + -8 = -1.1443454 u = -1.1443454 Simplifying u = -1.1443454Subproblem 2
u + 8 = -6.8556546 Simplifying u + 8 = -6.8556546 Reorder the terms: 8 + u = -6.8556546 Solving 8 + u = -6.8556546 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = -6.8556546 + -8 Combine like terms: 8 + -8 = 0 0 + u = -6.8556546 + -8 u = -6.8556546 + -8 Combine like terms: -6.8556546 + -8 = -14.8556546 u = -14.8556546 Simplifying u = -14.8556546Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.1443454, -14.8556546}Solution
u = {-1.1443454, -14.8556546}
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