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Simplifying u + -1 + u + -1 + 2u2 + -5u + -9 = 0 Reorder the terms: -1 + -1 + -9 + u + u + -5u + 2u2 = 0 Combine like terms: -1 + -1 = -2 -2 + -9 + u + u + -5u + 2u2 = 0 Combine like terms: -2 + -9 = -11 -11 + u + u + -5u + 2u2 = 0 Combine like terms: u + u = 2u -11 + 2u + -5u + 2u2 = 0 Combine like terms: 2u + -5u = -3u -11 + -3u + 2u2 = 0 Solving -11 + -3u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -1.5u + u2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -1.5u + 5.5 + u2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -1.5u + u2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -1.5u + u2 = 0 + 5.5 -1.5u + u2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -1.5u + u2 = 5.5 The u term is -1.5u. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5u + 0.5625 + u2 = 5.5 + 0.5625 Reorder the terms: 0.5625 + -1.5u + u2 = 5.5 + 0.5625 Combine like terms: 5.5 + 0.5625 = 6.0625 0.5625 + -1.5u + u2 = 6.0625 Factor a perfect square on the left side: (u + -0.75)(u + -0.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (u + -0.75) equal to 2.46221445 and -2.46221445.Subproblem 1
u + -0.75 = 2.46221445 Simplifying u + -0.75 = 2.46221445 Reorder the terms: -0.75 + u = 2.46221445 Solving -0.75 + u = 2.46221445 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + u = 2.46221445 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + u = 2.46221445 + 0.75 u = 2.46221445 + 0.75 Combine like terms: 2.46221445 + 0.75 = 3.21221445 u = 3.21221445 Simplifying u = 3.21221445Subproblem 2
u + -0.75 = -2.46221445 Simplifying u + -0.75 = -2.46221445 Reorder the terms: -0.75 + u = -2.46221445 Solving -0.75 + u = -2.46221445 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + u = -2.46221445 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + u = -2.46221445 + 0.75 u = -2.46221445 + 0.75 Combine like terms: -2.46221445 + 0.75 = -1.71221445 u = -1.71221445 Simplifying u = -1.71221445Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.21221445, -1.71221445}
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