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Simplifying (u2) + 25 = 2(u2) + -8u + 1 u2 + 25 = 2(u2) + -8u + 1 Reorder the terms: 25 + u2 = 2(u2) + -8u + 1 Reorder the terms: 25 + u2 = 1 + -8u + 2u2 Solving 25 + u2 = 1 + -8u + 2u2 Solving for variable 'u'. Reorder the terms: 25 + -1 + 8u + u2 + -2u2 = 1 + -8u + 2u2 + -1 + 8u + -2u2 Combine like terms: 25 + -1 = 24 24 + 8u + u2 + -2u2 = 1 + -8u + 2u2 + -1 + 8u + -2u2 Combine like terms: u2 + -2u2 = -1u2 24 + 8u + -1u2 = 1 + -8u + 2u2 + -1 + 8u + -2u2 Reorder the terms: 24 + 8u + -1u2 = 1 + -1 + -8u + 8u + 2u2 + -2u2 Combine like terms: 1 + -1 = 0 24 + 8u + -1u2 = 0 + -8u + 8u + 2u2 + -2u2 24 + 8u + -1u2 = -8u + 8u + 2u2 + -2u2 Combine like terms: -8u + 8u = 0 24 + 8u + -1u2 = 0 + 2u2 + -2u2 24 + 8u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 24 + 8u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + -8u + u2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -8u + 24 + u2 = 0 + 24 Reorder the terms: -24 + 24 + -8u + u2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -8u + u2 = 0 + 24 -8u + u2 = 0 + 24 Combine like terms: 0 + 24 = 24 -8u + u2 = 24 The u term is -8u. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8u + 16 + u2 = 24 + 16 Reorder the terms: 16 + -8u + u2 = 24 + 16 Combine like terms: 24 + 16 = 40 16 + -8u + u2 = 40 Factor a perfect square on the left side: (u + -4)(u + -4) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (u + -4) equal to 6.32455532 and -6.32455532.Subproblem 1
u + -4 = 6.32455532 Simplifying u + -4 = 6.32455532 Reorder the terms: -4 + u = 6.32455532 Solving -4 + u = 6.32455532 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = 6.32455532 + 4 Combine like terms: -4 + 4 = 0 0 + u = 6.32455532 + 4 u = 6.32455532 + 4 Combine like terms: 6.32455532 + 4 = 10.32455532 u = 10.32455532 Simplifying u = 10.32455532Subproblem 2
u + -4 = -6.32455532 Simplifying u + -4 = -6.32455532 Reorder the terms: -4 + u = -6.32455532 Solving -4 + u = -6.32455532 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = -6.32455532 + 4 Combine like terms: -4 + 4 = 0 0 + u = -6.32455532 + 4 u = -6.32455532 + 4 Combine like terms: -6.32455532 + 4 = -2.32455532 u = -2.32455532 Simplifying u = -2.32455532Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.32455532, -2.32455532}
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