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Simplifying 8u2 + -8u + -1 = 0 Reorder the terms: -1 + -8u + 8u2 = 0 Solving -1 + -8u + 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'. -0.125 + -1u + u2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1u + 0.125 + u2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1u + u2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1u + u2 = 0 + 0.125 -1u + u2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1u + u2 = 0.125 The u term is -1u. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1u + 0.25 + u2 = 0.125 + 0.25 Reorder the terms: 0.25 + -1u + u2 = 0.125 + 0.25 Combine like terms: 0.125 + 0.25 = 0.375 0.25 + -1u + u2 = 0.375 Factor a perfect square on the left side: (u + -0.5)(u + -0.5) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (u + -0.5) equal to 0.612372436 and -0.612372436.Subproblem 1
u + -0.5 = 0.612372436 Simplifying u + -0.5 = 0.612372436 Reorder the terms: -0.5 + u = 0.612372436 Solving -0.5 + u = 0.612372436 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + u = 0.612372436 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + u = 0.612372436 + 0.5 u = 0.612372436 + 0.5 Combine like terms: 0.612372436 + 0.5 = 1.112372436 u = 1.112372436 Simplifying u = 1.112372436Subproblem 2
u + -0.5 = -0.612372436 Simplifying u + -0.5 = -0.612372436 Reorder the terms: -0.5 + u = -0.612372436 Solving -0.5 + u = -0.612372436 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + u = -0.612372436 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + u = -0.612372436 + 0.5 u = -0.612372436 + 0.5 Combine like terms: -0.612372436 + 0.5 = -0.112372436 u = -0.112372436 Simplifying u = -0.112372436Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.112372436, -0.112372436}
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