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Simplifying (-2u2 + 3u) + (-6u2 + -4u + 1) = 0 Reorder the terms: (3u + -2u2) + (-6u2 + -4u + 1) = 0 Remove parenthesis around (3u + -2u2) 3u + -2u2 + (-6u2 + -4u + 1) = 0 Reorder the terms: 3u + -2u2 + (1 + -4u + -6u2) = 0 Remove parenthesis around (1 + -4u + -6u2) 3u + -2u2 + 1 + -4u + -6u2 = 0 Reorder the terms: 1 + 3u + -4u + -2u2 + -6u2 = 0 Combine like terms: 3u + -4u = -1u 1 + -1u + -2u2 + -6u2 = 0 Combine like terms: -2u2 + -6u2 = -8u2 1 + -1u + -8u2 = 0 Solving 1 + -1u + -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 + 0.125u + u2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.125u + 0.125 + u2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.125u + u2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.125u + u2 = 0 + 0.125 0.125u + u2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.125u + u2 = 0.125 The u term is 0.125u. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125u + 0.00390625 + u2 = 0.125 + 0.00390625 Reorder the terms: 0.00390625 + 0.125u + u2 = 0.125 + 0.00390625 Combine like terms: 0.125 + 0.00390625 = 0.12890625 0.00390625 + 0.125u + u2 = 0.12890625 Factor a perfect square on the left side: (u + 0.0625)(u + 0.0625) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (u + 0.0625) equal to 0.359035165 and -0.359035165.Subproblem 1
u + 0.0625 = 0.359035165 Simplifying u + 0.0625 = 0.359035165 Reorder the terms: 0.0625 + u = 0.359035165 Solving 0.0625 + u = 0.359035165 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + u = 0.359035165 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + u = 0.359035165 + -0.0625 u = 0.359035165 + -0.0625 Combine like terms: 0.359035165 + -0.0625 = 0.296535165 u = 0.296535165 Simplifying u = 0.296535165Subproblem 2
u + 0.0625 = -0.359035165 Simplifying u + 0.0625 = -0.359035165 Reorder the terms: 0.0625 + u = -0.359035165 Solving 0.0625 + u = -0.359035165 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + u = -0.359035165 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + u = -0.359035165 + -0.0625 u = -0.359035165 + -0.0625 Combine like terms: -0.359035165 + -0.0625 = -0.421535165 u = -0.421535165 Simplifying u = -0.421535165Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.296535165, -0.421535165}
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