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Simplifying 9u2 + -4u + -6 = 0 Reorder the terms: -6 + -4u + 9u2 = 0 Solving -6 + -4u + 9u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + -0.4444444444u + u2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.4444444444u + 0.6666666667 + u2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.4444444444u + u2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.4444444444u + u2 = 0 + 0.6666666667 -0.4444444444u + u2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.4444444444u + u2 = 0.6666666667 The u term is -0.4444444444u. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444u + 0.04938271604 + u2 = 0.6666666667 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444u + u2 = 0.6666666667 + 0.04938271604 Combine like terms: 0.6666666667 + 0.04938271604 = 0.71604938274 0.04938271604 + -0.4444444444u + u2 = 0.71604938274 Factor a perfect square on the left side: (u + -0.2222222222)(u + -0.2222222222) = 0.71604938274 Calculate the square root of the right side: 0.846197012 Break this problem into two subproblems by setting (u + -0.2222222222) equal to 0.846197012 and -0.846197012.Subproblem 1
u + -0.2222222222 = 0.846197012 Simplifying u + -0.2222222222 = 0.846197012 Reorder the terms: -0.2222222222 + u = 0.846197012 Solving -0.2222222222 + u = 0.846197012 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + u = 0.846197012 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + u = 0.846197012 + 0.2222222222 u = 0.846197012 + 0.2222222222 Combine like terms: 0.846197012 + 0.2222222222 = 1.0684192342 u = 1.0684192342 Simplifying u = 1.0684192342Subproblem 2
u + -0.2222222222 = -0.846197012 Simplifying u + -0.2222222222 = -0.846197012 Reorder the terms: -0.2222222222 + u = -0.846197012 Solving -0.2222222222 + u = -0.846197012 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + u = -0.846197012 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + u = -0.846197012 + 0.2222222222 u = -0.846197012 + 0.2222222222 Combine like terms: -0.846197012 + 0.2222222222 = -0.6239747898 u = -0.6239747898 Simplifying u = -0.6239747898Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.0684192342, -0.6239747898}
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