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Simplifying -5u = -8u2 + 1 Reorder the terms: -5u = 1 + -8u2 Solving -5u = 1 + -8u2 Solving for variable 'u'. Reorder the terms: -1 + -5u + 8u2 = 1 + -8u2 + -1 + 8u2 Reorder the terms: -1 + -5u + 8u2 = 1 + -1 + -8u2 + 8u2 Combine like terms: 1 + -1 = 0 -1 + -5u + 8u2 = 0 + -8u2 + 8u2 -1 + -5u + 8u2 = -8u2 + 8u2 Combine like terms: -8u2 + 8u2 = 0 -1 + -5u + 8u2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.625u + u2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.625u + 0.125 + u2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.625u + u2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.625u + u2 = 0 + 0.125 -0.625u + u2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.625u + u2 = 0.125 The u term is -0.625u. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625u + 0.09765625 + u2 = 0.125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625u + u2 = 0.125 + 0.09765625 Combine like terms: 0.125 + 0.09765625 = 0.22265625 0.09765625 + -0.625u + u2 = 0.22265625 Factor a perfect square on the left side: (u + -0.3125)(u + -0.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (u + -0.3125) equal to 0.471864652 and -0.471864652.Subproblem 1
u + -0.3125 = 0.471864652 Simplifying u + -0.3125 = 0.471864652 Reorder the terms: -0.3125 + u = 0.471864652 Solving -0.3125 + u = 0.471864652 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + u = 0.471864652 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + u = 0.471864652 + 0.3125 u = 0.471864652 + 0.3125 Combine like terms: 0.471864652 + 0.3125 = 0.784364652 u = 0.784364652 Simplifying u = 0.784364652Subproblem 2
u + -0.3125 = -0.471864652 Simplifying u + -0.3125 = -0.471864652 Reorder the terms: -0.3125 + u = -0.471864652 Solving -0.3125 + u = -0.471864652 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + u = -0.471864652 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + u = -0.471864652 + 0.3125 u = -0.471864652 + 0.3125 Combine like terms: -0.471864652 + 0.3125 = -0.159364652 u = -0.159364652 Simplifying u = -0.159364652Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.784364652, -0.159364652}
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