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Simplifying -1u2 + 9u + 26 = 0 Reorder the terms: 26 + 9u + -1u2 = 0 Solving 26 + 9u + -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'. -26 + -9u + u2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -9u + 26 + u2 = 0 + 26 Reorder the terms: -26 + 26 + -9u + u2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -9u + u2 = 0 + 26 -9u + u2 = 0 + 26 Combine like terms: 0 + 26 = 26 -9u + u2 = 26 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 = 26 + 20.25 Reorder the terms: 20.25 + -9u + u2 = 26 + 20.25 Combine like terms: 26 + 20.25 = 46.25 20.25 + -9u + u2 = 46.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (u + -4.5) equal to 6.800735254 and -6.800735254.Subproblem 1
u + -4.5 = 6.800735254 Simplifying u + -4.5 = 6.800735254 Reorder the terms: -4.5 + u = 6.800735254 Solving -4.5 + u = 6.800735254 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 = 6.800735254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 6.800735254 + 4.5 u = 6.800735254 + 4.5 Combine like terms: 6.800735254 + 4.5 = 11.300735254 u = 11.300735254 Simplifying u = 11.300735254Subproblem 2
u + -4.5 = -6.800735254 Simplifying u + -4.5 = -6.800735254 Reorder the terms: -4.5 + u = -6.800735254 Solving -4.5 + u = -6.800735254 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 = -6.800735254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -6.800735254 + 4.5 u = -6.800735254 + 4.5 Combine like terms: -6.800735254 + 4.5 = -2.300735254 u = -2.300735254 Simplifying u = -2.300735254Solution
The solution to the problem is based on the solutions from the subproblems. u = {11.300735254, -2.300735254}
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