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Simplifying u2 + 12u + -36 = 0 Reorder the terms: -36 + 12u + u2 = 0 Solving -36 + 12u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 12u + 36 + u2 = 0 + 36 Reorder the terms: -36 + 36 + 12u + u2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 12u + u2 = 0 + 36 12u + u2 = 0 + 36 Combine like terms: 0 + 36 = 36 12u + u2 = 36 The u term is 12u. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12u + 36 + u2 = 36 + 36 Reorder the terms: 36 + 12u + u2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + 12u + u2 = 72 Factor a perfect square on the left side: (u + 6)(u + 6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (u + 6) equal to 8.485281374 and -8.485281374.Subproblem 1
u + 6 = 8.485281374 Simplifying u + 6 = 8.485281374 Reorder the terms: 6 + u = 8.485281374 Solving 6 + u = 8.485281374 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + u = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + u = 8.485281374 + -6 u = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 u = 2.485281374 Simplifying u = 2.485281374Subproblem 2
u + 6 = -8.485281374 Simplifying u + 6 = -8.485281374 Reorder the terms: 6 + u = -8.485281374 Solving 6 + u = -8.485281374 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + u = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + u = -8.485281374 + -6 u = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 u = -14.485281374 Simplifying u = -14.485281374Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.485281374, -14.485281374}
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