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Simplifying 5u2 + 9u = 4 Reorder the terms: 9u + 5u2 = 4 Solving 9u + 5u2 = 4 Solving for variable 'u'. Reorder the terms: -4 + 9u + 5u2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 9u + 5u2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 1.8u + u2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 1.8u + 0.8 + u2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 1.8u + u2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1.8u + u2 = 0 + 0.8 1.8u + u2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 1.8u + u2 = 0.8 The u term is 1.8u. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8u + 0.81 + u2 = 0.8 + 0.81 Reorder the terms: 0.81 + 1.8u + u2 = 0.8 + 0.81 Combine like terms: 0.8 + 0.81 = 1.61 0.81 + 1.8u + u2 = 1.61 Factor a perfect square on the left side: (u + 0.9)(u + 0.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (u + 0.9) equal to 1.268857754 and -1.268857754.Subproblem 1
u + 0.9 = 1.268857754 Simplifying u + 0.9 = 1.268857754 Reorder the terms: 0.9 + u = 1.268857754 Solving 0.9 + u = 1.268857754 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + u = 1.268857754 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + u = 1.268857754 + -0.9 u = 1.268857754 + -0.9 Combine like terms: 1.268857754 + -0.9 = 0.368857754 u = 0.368857754 Simplifying u = 0.368857754Subproblem 2
u + 0.9 = -1.268857754 Simplifying u + 0.9 = -1.268857754 Reorder the terms: 0.9 + u = -1.268857754 Solving 0.9 + u = -1.268857754 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + u = -1.268857754 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + u = -1.268857754 + -0.9 u = -1.268857754 + -0.9 Combine like terms: -1.268857754 + -0.9 = -2.168857754 u = -2.168857754 Simplifying u = -2.168857754Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.368857754, -2.168857754}
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