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Simplifying u2 + 3u + -25 = 0 Reorder the terms: -25 + 3u + u2 = 0 Solving -25 + 3u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 3u + 25 + u2 = 0 + 25 Reorder the terms: -25 + 25 + 3u + u2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 3u + u2 = 0 + 25 3u + u2 = 0 + 25 Combine like terms: 0 + 25 = 25 3u + u2 = 25 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 = 25 + 2.25 Reorder the terms: 2.25 + 3u + u2 = 25 + 2.25 Combine like terms: 25 + 2.25 = 27.25 2.25 + 3u + u2 = 27.25 Factor a perfect square on the left side: (u + 1.5)(u + 1.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (u + 1.5) equal to 5.220153254 and -5.220153254.Subproblem 1
u + 1.5 = 5.220153254 Simplifying u + 1.5 = 5.220153254 Reorder the terms: 1.5 + u = 5.220153254 Solving 1.5 + u = 5.220153254 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 = 5.220153254 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = 5.220153254 + -1.5 u = 5.220153254 + -1.5 Combine like terms: 5.220153254 + -1.5 = 3.720153254 u = 3.720153254 Simplifying u = 3.720153254Subproblem 2
u + 1.5 = -5.220153254 Simplifying u + 1.5 = -5.220153254 Reorder the terms: 1.5 + u = -5.220153254 Solving 1.5 + u = -5.220153254 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 = -5.220153254 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = -5.220153254 + -1.5 u = -5.220153254 + -1.5 Combine like terms: -5.220153254 + -1.5 = -6.720153254 u = -6.720153254 Simplifying u = -6.720153254Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.720153254, -6.720153254}
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