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Simplifying 8u2 + -31u + -5 = 0 Reorder the terms: -5 + -31u + 8u2 = 0 Solving -5 + -31u + 8u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -3.875u + u2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -3.875u + 0.625 + u2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -3.875u + u2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -3.875u + u2 = 0 + 0.625 -3.875u + u2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -3.875u + u2 = 0.625 The u term is -3.875u. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875u + 3.75390625 + u2 = 0.625 + 3.75390625 Reorder the terms: 3.75390625 + -3.875u + u2 = 0.625 + 3.75390625 Combine like terms: 0.625 + 3.75390625 = 4.37890625 3.75390625 + -3.875u + u2 = 4.37890625 Factor a perfect square on the left side: (u + -1.9375)(u + -1.9375) = 4.37890625 Calculate the square root of the right side: 2.09258363 Break this problem into two subproblems by setting (u + -1.9375) equal to 2.09258363 and -2.09258363.Subproblem 1
u + -1.9375 = 2.09258363 Simplifying u + -1.9375 = 2.09258363 Reorder the terms: -1.9375 + u = 2.09258363 Solving -1.9375 + u = 2.09258363 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + u = 2.09258363 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + u = 2.09258363 + 1.9375 u = 2.09258363 + 1.9375 Combine like terms: 2.09258363 + 1.9375 = 4.03008363 u = 4.03008363 Simplifying u = 4.03008363Subproblem 2
u + -1.9375 = -2.09258363 Simplifying u + -1.9375 = -2.09258363 Reorder the terms: -1.9375 + u = -2.09258363 Solving -1.9375 + u = -2.09258363 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + u = -2.09258363 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + u = -2.09258363 + 1.9375 u = -2.09258363 + 1.9375 Combine like terms: -2.09258363 + 1.9375 = -0.15508363 u = -0.15508363 Simplifying u = -0.15508363Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.03008363, -0.15508363}
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