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Simplifying u2 + -16u + 3 = 0 Reorder the terms: 3 + -16u + u2 = 0 Solving 3 + -16u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -16u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -16u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -16u + u2 = 0 + -3 -16u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -16u + u2 = -3 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 = -3 + 64 Reorder the terms: 64 + -16u + u2 = -3 + 64 Combine like terms: -3 + 64 = 61 64 + -16u + u2 = 61 Factor a perfect square on the left side: (u + -8)(u + -8) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (u + -8) equal to 7.810249676 and -7.810249676.Subproblem 1
u + -8 = 7.810249676 Simplifying u + -8 = 7.810249676 Reorder the terms: -8 + u = 7.810249676 Solving -8 + u = 7.810249676 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 = 7.810249676 + 8 Combine like terms: -8 + 8 = 0 0 + u = 7.810249676 + 8 u = 7.810249676 + 8 Combine like terms: 7.810249676 + 8 = 15.810249676 u = 15.810249676 Simplifying u = 15.810249676Subproblem 2
u + -8 = -7.810249676 Simplifying u + -8 = -7.810249676 Reorder the terms: -8 + u = -7.810249676 Solving -8 + u = -7.810249676 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 = -7.810249676 + 8 Combine like terms: -8 + 8 = 0 0 + u = -7.810249676 + 8 u = -7.810249676 + 8 Combine like terms: -7.810249676 + 8 = 0.189750324 u = 0.189750324 Simplifying u = 0.189750324Solution
The solution to the problem is based on the solutions from the subproblems. u = {15.810249676, 0.189750324}
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