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Simplifying 2u2 + 5u + -26 + -1u2 + -2u + -4 = 0 Reorder the terms: -26 + -4 + 5u + -2u + 2u2 + -1u2 = 0 Combine like terms: -26 + -4 = -30 -30 + 5u + -2u + 2u2 + -1u2 = 0 Combine like terms: 5u + -2u = 3u -30 + 3u + 2u2 + -1u2 = 0 Combine like terms: 2u2 + -1u2 = 1u2 -30 + 3u + 1u2 = 0 Solving -30 + 3u + 1u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 3u + 30 + u2 = 0 + 30 Reorder the terms: -30 + 30 + 3u + u2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3u + u2 = 0 + 30 3u + u2 = 0 + 30 Combine like terms: 0 + 30 = 30 3u + u2 = 30 The u term is 3u. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3u + 2.25 + u2 = 30 + 2.25 Reorder the terms: 2.25 + 3u + u2 = 30 + 2.25 Combine like terms: 30 + 2.25 = 32.25 2.25 + 3u + u2 = 32.25 Factor a perfect square on the left side: (u + 1.5)(u + 1.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (u + 1.5) equal to 5.678908346 and -5.678908346.Subproblem 1
u + 1.5 = 5.678908346 Simplifying u + 1.5 = 5.678908346 Reorder the terms: 1.5 + u = 5.678908346 Solving 1.5 + u = 5.678908346 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + u = 5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = 5.678908346 + -1.5 u = 5.678908346 + -1.5 Combine like terms: 5.678908346 + -1.5 = 4.178908346 u = 4.178908346 Simplifying u = 4.178908346Subproblem 2
u + 1.5 = -5.678908346 Simplifying u + 1.5 = -5.678908346 Reorder the terms: 1.5 + u = -5.678908346 Solving 1.5 + u = -5.678908346 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + u = -5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = -5.678908346 + -1.5 u = -5.678908346 + -1.5 Combine like terms: -5.678908346 + -1.5 = -7.178908346 u = -7.178908346 Simplifying u = -7.178908346Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.178908346, -7.178908346}
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