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Simplifying 5u2 + (-9u) + 2 = 0 Reorder the terms: 2 + (-9u) + 5u2 = 0 Solving 2 + (-9u) + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + (-1.8u) + u2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + (-1.8u) + -0.4 + u2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + (-1.8u) + u2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + (-1.8u) + u2 = 0 + -0.4 (-1.8u) + u2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 (-1.8u) + u2 = -0.4 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 = -0.4 + 0.81 Reorder the terms: 0.81 + (-1.8u) + u2 = -0.4 + 0.81 Combine like terms: -0.4 + 0.81 = 0.41 0.81 + (-1.8u) + u2 = 0.41 Factor a perfect square on the left side: (u + -0.9)(u + -0.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (u + -0.9) equal to 0.640312424 and -0.640312424.Subproblem 1
u + -0.9 = 0.640312424 Simplifying u + -0.9 = 0.640312424 Reorder the terms: -0.9 + u = 0.640312424 Solving -0.9 + u = 0.640312424 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 = 0.640312424 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + u = 0.640312424 + 0.9 u = 0.640312424 + 0.9 Combine like terms: 0.640312424 + 0.9 = 1.540312424 u = 1.540312424 Simplifying u = 1.540312424Subproblem 2
u + -0.9 = -0.640312424 Simplifying u + -0.9 = -0.640312424 Reorder the terms: -0.9 + u = -0.640312424 Solving -0.9 + u = -0.640312424 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 = -0.640312424 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + u = -0.640312424 + 0.9 u = -0.640312424 + 0.9 Combine like terms: -0.640312424 + 0.9 = 0.259687576 u = 0.259687576 Simplifying u = 0.259687576Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.540312424, 0.259687576}
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