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Simplifying 4u2 + -3u + -8 = 0 Reorder the terms: -8 + -3u + 4u2 = 0 Solving -8 + -3u + 4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -0.75u + u2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.75u + 2 + u2 = 0 + 2 Reorder the terms: -2 + 2 + -0.75u + u2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.75u + u2 = 0 + 2 -0.75u + u2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.75u + u2 = 2 The u term is -0.75u. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75u + 0.140625 + u2 = 2 + 0.140625 Reorder the terms: 0.140625 + -0.75u + u2 = 2 + 0.140625 Combine like terms: 2 + 0.140625 = 2.140625 0.140625 + -0.75u + u2 = 2.140625 Factor a perfect square on the left side: (u + -0.375)(u + -0.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (u + -0.375) equal to 1.463087489 and -1.463087489.Subproblem 1
u + -0.375 = 1.463087489 Simplifying u + -0.375 = 1.463087489 Reorder the terms: -0.375 + u = 1.463087489 Solving -0.375 + u = 1.463087489 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + u = 1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + u = 1.463087489 + 0.375 u = 1.463087489 + 0.375 Combine like terms: 1.463087489 + 0.375 = 1.838087489 u = 1.838087489 Simplifying u = 1.838087489Subproblem 2
u + -0.375 = -1.463087489 Simplifying u + -0.375 = -1.463087489 Reorder the terms: -0.375 + u = -1.463087489 Solving -0.375 + u = -1.463087489 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + u = -1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + u = -1.463087489 + 0.375 u = -1.463087489 + 0.375 Combine like terms: -1.463087489 + 0.375 = -1.088087489 u = -1.088087489 Simplifying u = -1.088087489Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.838087489, -1.088087489}
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