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Simplifying u2 + 9u + -6 = 0 Reorder the terms: -6 + 9u + u2 = 0 Solving -6 + 9u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 9u + 6 + u2 = 0 + 6 Reorder the terms: -6 + 6 + 9u + u2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 9u + u2 = 0 + 6 9u + u2 = 0 + 6 Combine like terms: 0 + 6 = 6 9u + u2 = 6 The u term is 9u. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9u + 20.25 + u2 = 6 + 20.25 Reorder the terms: 20.25 + 9u + u2 = 6 + 20.25 Combine like terms: 6 + 20.25 = 26.25 20.25 + 9u + u2 = 26.25 Factor a perfect square on the left side: (u + 4.5)(u + 4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (u + 4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
u + 4.5 = 5.123475383 Simplifying u + 4.5 = 5.123475383 Reorder the terms: 4.5 + u = 5.123475383 Solving 4.5 + u = 5.123475383 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = 5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = 5.123475383 + -4.5 u = 5.123475383 + -4.5 Combine like terms: 5.123475383 + -4.5 = 0.623475383 u = 0.623475383 Simplifying u = 0.623475383Subproblem 2
u + 4.5 = -5.123475383 Simplifying u + 4.5 = -5.123475383 Reorder the terms: 4.5 + u = -5.123475383 Solving 4.5 + u = -5.123475383 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = -5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = -5.123475383 + -4.5 u = -5.123475383 + -4.5 Combine like terms: -5.123475383 + -4.5 = -9.623475383 u = -9.623475383 Simplifying u = -9.623475383Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.623475383, -9.623475383}
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