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Simplifying (3u2 + 2u + -1) + -1(-6u2 + 2u + 2) + (6u2 + 9u + 2) = 0 Reorder the terms: (-1 + 2u + 3u2) + -1(-6u2 + 2u + 2) + (6u2 + 9u + 2) = 0 Remove parenthesis around (-1 + 2u + 3u2) -1 + 2u + 3u2 + -1(-6u2 + 2u + 2) + (6u2 + 9u + 2) = 0 Reorder the terms: -1 + 2u + 3u2 + -1(2 + 2u + -6u2) + (6u2 + 9u + 2) = 0 -1 + 2u + 3u2 + (2 * -1 + 2u * -1 + -6u2 * -1) + (6u2 + 9u + 2) = 0 -1 + 2u + 3u2 + (-2 + -2u + 6u2) + (6u2 + 9u + 2) = 0 Reorder the terms: -1 + 2u + 3u2 + -2 + -2u + 6u2 + (2 + 9u + 6u2) = 0 Remove parenthesis around (2 + 9u + 6u2) -1 + 2u + 3u2 + -2 + -2u + 6u2 + 2 + 9u + 6u2 = 0 Reorder the terms: -1 + -2 + 2 + 2u + -2u + 9u + 3u2 + 6u2 + 6u2 = 0 Combine like terms: -1 + -2 = -3 -3 + 2 + 2u + -2u + 9u + 3u2 + 6u2 + 6u2 = 0 Combine like terms: -3 + 2 = -1 -1 + 2u + -2u + 9u + 3u2 + 6u2 + 6u2 = 0 Combine like terms: 2u + -2u = 0 -1 + 0 + 9u + 3u2 + 6u2 + 6u2 = 0 -1 + 9u + 3u2 + 6u2 + 6u2 = 0 Combine like terms: 3u2 + 6u2 = 9u2 -1 + 9u + 9u2 + 6u2 = 0 Combine like terms: 9u2 + 6u2 = 15u2 -1 + 9u + 15u2 = 0 Solving -1 + 9u + 15u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.06666666667 + 0.6u + u2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + 0.6u + 0.06666666667 + u2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + 0.6u + u2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + 0.6u + u2 = 0 + 0.06666666667 0.6u + u2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 0.6u + u2 = 0.06666666667 The u term is 0.6u. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6u + 0.09 + u2 = 0.06666666667 + 0.09 Reorder the terms: 0.09 + 0.6u + u2 = 0.06666666667 + 0.09 Combine like terms: 0.06666666667 + 0.09 = 0.15666666667 0.09 + 0.6u + u2 = 0.15666666667 Factor a perfect square on the left side: (u + 0.3)(u + 0.3) = 0.15666666667 Calculate the square root of the right side: 0.395811403 Break this problem into two subproblems by setting (u + 0.3) equal to 0.395811403 and -0.395811403.Subproblem 1
u + 0.3 = 0.395811403 Simplifying u + 0.3 = 0.395811403 Reorder the terms: 0.3 + u = 0.395811403 Solving 0.3 + u = 0.395811403 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + u = 0.395811403 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + u = 0.395811403 + -0.3 u = 0.395811403 + -0.3 Combine like terms: 0.395811403 + -0.3 = 0.095811403 u = 0.095811403 Simplifying u = 0.095811403Subproblem 2
u + 0.3 = -0.395811403 Simplifying u + 0.3 = -0.395811403 Reorder the terms: 0.3 + u = -0.395811403 Solving 0.3 + u = -0.395811403 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + u = -0.395811403 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + u = -0.395811403 + -0.3 u = -0.395811403 + -0.3 Combine like terms: -0.395811403 + -0.3 = -0.695811403 u = -0.695811403 Simplifying u = -0.695811403Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.095811403, -0.695811403}
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