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Simplifying u2 + -16u + 24 = 0 Reorder the terms: 24 + -16u + u2 = 0 Solving 24 + -16u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -16u + -24 + u2 = 0 + -24 Reorder the terms: 24 + -24 + -16u + u2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -16u + u2 = 0 + -24 -16u + u2 = 0 + -24 Combine like terms: 0 + -24 = -24 -16u + u2 = -24 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 = -24 + 64 Reorder the terms: 64 + -16u + u2 = -24 + 64 Combine like terms: -24 + 64 = 40 64 + -16u + u2 = 40 Factor a perfect square on the left side: (u + -8)(u + -8) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (u + -8) equal to 6.32455532 and -6.32455532.Subproblem 1
u + -8 = 6.32455532 Simplifying u + -8 = 6.32455532 Reorder the terms: -8 + u = 6.32455532 Solving -8 + u = 6.32455532 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 = 6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + u = 6.32455532 + 8 u = 6.32455532 + 8 Combine like terms: 6.32455532 + 8 = 14.32455532 u = 14.32455532 Simplifying u = 14.32455532Subproblem 2
u + -8 = -6.32455532 Simplifying u + -8 = -6.32455532 Reorder the terms: -8 + u = -6.32455532 Solving -8 + u = -6.32455532 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 = -6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + u = -6.32455532 + 8 u = -6.32455532 + 8 Combine like terms: -6.32455532 + 8 = 1.67544468 u = 1.67544468 Simplifying u = 1.67544468Solution
The solution to the problem is based on the solutions from the subproblems. u = {14.32455532, 1.67544468}
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