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Simplifying -1u2 + 8u + 12 = 0 Reorder the terms: 12 + 8u + -1u2 = 0 Solving 12 + 8u + -1u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -8u + u2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -8u + 12 + u2 = 0 + 12 Reorder the terms: -12 + 12 + -8u + u2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -8u + u2 = 0 + 12 -8u + u2 = 0 + 12 Combine like terms: 0 + 12 = 12 -8u + u2 = 12 The u term is -8u. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8u + 16 + u2 = 12 + 16 Reorder the terms: 16 + -8u + u2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + -8u + u2 = 28 Factor a perfect square on the left side: (u + -4)(u + -4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (u + -4) equal to 5.291502622 and -5.291502622.Subproblem 1
u + -4 = 5.291502622 Simplifying u + -4 = 5.291502622 Reorder the terms: -4 + u = 5.291502622 Solving -4 + u = 5.291502622 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = 5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + u = 5.291502622 + 4 u = 5.291502622 + 4 Combine like terms: 5.291502622 + 4 = 9.291502622 u = 9.291502622 Simplifying u = 9.291502622Subproblem 2
u + -4 = -5.291502622 Simplifying u + -4 = -5.291502622 Reorder the terms: -4 + u = -5.291502622 Solving -4 + u = -5.291502622 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = -5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + u = -5.291502622 + 4 u = -5.291502622 + 4 Combine like terms: -5.291502622 + 4 = -1.291502622 u = -1.291502622 Simplifying u = -1.291502622Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.291502622, -1.291502622}
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