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Simplifying 2u2 + 5u + -26 + -2u + -2 = 0 Reorder the terms: -26 + -2 + 5u + -2u + 2u2 = 0 Combine like terms: -26 + -2 = -28 -28 + 5u + -2u + 2u2 = 0 Combine like terms: 5u + -2u = 3u -28 + 3u + 2u2 = 0 Solving -28 + 3u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 1.5u + u2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 1.5u + 14 + u2 = 0 + 14 Reorder the terms: -14 + 14 + 1.5u + u2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 1.5u + u2 = 0 + 14 1.5u + u2 = 0 + 14 Combine like terms: 0 + 14 = 14 1.5u + u2 = 14 The u term is 1.5u. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5u + 0.5625 + u2 = 14 + 0.5625 Reorder the terms: 0.5625 + 1.5u + u2 = 14 + 0.5625 Combine like terms: 14 + 0.5625 = 14.5625 0.5625 + 1.5u + u2 = 14.5625 Factor a perfect square on the left side: (u + 0.75)(u + 0.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (u + 0.75) equal to 3.816084381 and -3.816084381.Subproblem 1
u + 0.75 = 3.816084381 Simplifying u + 0.75 = 3.816084381 Reorder the terms: 0.75 + u = 3.816084381 Solving 0.75 + u = 3.816084381 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + u = 3.816084381 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + u = 3.816084381 + -0.75 u = 3.816084381 + -0.75 Combine like terms: 3.816084381 + -0.75 = 3.066084381 u = 3.066084381 Simplifying u = 3.066084381Subproblem 2
u + 0.75 = -3.816084381 Simplifying u + 0.75 = -3.816084381 Reorder the terms: 0.75 + u = -3.816084381 Solving 0.75 + u = -3.816084381 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + u = -3.816084381 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + u = -3.816084381 + -0.75 u = -3.816084381 + -0.75 Combine like terms: -3.816084381 + -0.75 = -4.566084381 u = -4.566084381 Simplifying u = -4.566084381Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.066084381, -4.566084381}
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