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Simplifying u2 + -16u + 10 = 0 Reorder the terms: 10 + -16u + u2 = 0 Solving 10 + -16u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -16u + -10 + u2 = 0 + -10 Reorder the terms: 10 + -10 + -16u + u2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -16u + u2 = 0 + -10 -16u + u2 = 0 + -10 Combine like terms: 0 + -10 = -10 -16u + u2 = -10 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 = -10 + 64 Reorder the terms: 64 + -16u + u2 = -10 + 64 Combine like terms: -10 + 64 = 54 64 + -16u + u2 = 54 Factor a perfect square on the left side: (u + -8)(u + -8) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (u + -8) equal to 7.348469228 and -7.348469228.Subproblem 1
u + -8 = 7.348469228 Simplifying u + -8 = 7.348469228 Reorder the terms: -8 + u = 7.348469228 Solving -8 + u = 7.348469228 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 = 7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + u = 7.348469228 + 8 u = 7.348469228 + 8 Combine like terms: 7.348469228 + 8 = 15.348469228 u = 15.348469228 Simplifying u = 15.348469228Subproblem 2
u + -8 = -7.348469228 Simplifying u + -8 = -7.348469228 Reorder the terms: -8 + u = -7.348469228 Solving -8 + u = -7.348469228 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 = -7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + u = -7.348469228 + 8 u = -7.348469228 + 8 Combine like terms: -7.348469228 + 8 = 0.651530772 u = 0.651530772 Simplifying u = 0.651530772Solution
The solution to the problem is based on the solutions from the subproblems. u = {15.348469228, 0.651530772}
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