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Simplifying u * 3 * 2u + u = 13 Reorder the terms for easier multiplication: 3 * 2u * u + u = 13 Multiply 3 * 2 6u * u + u = 13 Multiply u * u 6u2 + u = 13 Reorder the terms: u + 6u2 = 13 Solving u + 6u2 = 13 Solving for variable 'u'. Reorder the terms: -13 + u + 6u2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + u + 6u2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + 0.1666666667u + u2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + 0.1666666667u + 2.166666667 + u2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + 0.1666666667u + u2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + 0.1666666667u + u2 = 0 + 2.166666667 0.1666666667u + u2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 0.1666666667u + u2 = 2.166666667 The u term is u. 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. 0.1666666667u + 0.25 + u2 = 2.166666667 + 0.25 Reorder the terms: 0.25 + 0.1666666667u + u2 = 2.166666667 + 0.25 Combine like terms: 2.166666667 + 0.25 = 2.416666667 0.25 + 0.1666666667u + u2 = 2.416666667 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = 2.416666667 Calculate the square root of the right side: 1.554563176 Break this problem into two subproblems by setting (u + 0.5) equal to 1.554563176 and -1.554563176.Subproblem 1
u + 0.5 = 1.554563176 Simplifying u + 0.5 = 1.554563176 Reorder the terms: 0.5 + u = 1.554563176 Solving 0.5 + u = 1.554563176 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 = 1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = 1.554563176 + -0.5 u = 1.554563176 + -0.5 Combine like terms: 1.554563176 + -0.5 = 1.054563176 u = 1.054563176 Simplifying u = 1.054563176Subproblem 2
u + 0.5 = -1.554563176 Simplifying u + 0.5 = -1.554563176 Reorder the terms: 0.5 + u = -1.554563176 Solving 0.5 + u = -1.554563176 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 = -1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = -1.554563176 + -0.5 u = -1.554563176 + -0.5 Combine like terms: -1.554563176 + -0.5 = -2.054563176 u = -2.054563176 Simplifying u = -2.054563176Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.054563176, -2.054563176}
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