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Simplifying (2u2 + -1u + -6) + (5u2 + -7u + 3) = 0 Reorder the terms: (-6 + -1u + 2u2) + (5u2 + -7u + 3) = 0 Remove parenthesis around (-6 + -1u + 2u2) -6 + -1u + 2u2 + (5u2 + -7u + 3) = 0 Reorder the terms: -6 + -1u + 2u2 + (3 + -7u + 5u2) = 0 Remove parenthesis around (3 + -7u + 5u2) -6 + -1u + 2u2 + 3 + -7u + 5u2 = 0 Reorder the terms: -6 + 3 + -1u + -7u + 2u2 + 5u2 = 0 Combine like terms: -6 + 3 = -3 -3 + -1u + -7u + 2u2 + 5u2 = 0 Combine like terms: -1u + -7u = -8u -3 + -8u + 2u2 + 5u2 = 0 Combine like terms: 2u2 + 5u2 = 7u2 -3 + -8u + 7u2 = 0 Solving -3 + -8u + 7u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -1.142857143u + u2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1.142857143u + 0.4285714286 + u2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1.142857143u + u2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1.142857143u + u2 = 0 + 0.4285714286 -1.142857143u + u2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1.142857143u + u2 = 0.4285714286 The u term is -1.142857143u. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143u + 0.3265306123 + u2 = 0.4285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143u + u2 = 0.4285714286 + 0.3265306123 Combine like terms: 0.4285714286 + 0.3265306123 = 0.7551020409 0.3265306123 + -1.142857143u + u2 = 0.7551020409 Factor a perfect square on the left side: (u + -0.5714285715)(u + -0.5714285715) = 0.7551020409 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (u + -0.5714285715) equal to 0.868966076 and -0.868966076.Subproblem 1
u + -0.5714285715 = 0.868966076 Simplifying u + -0.5714285715 = 0.868966076 Reorder the terms: -0.5714285715 + u = 0.868966076 Solving -0.5714285715 + u = 0.868966076 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + u = 0.868966076 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + u = 0.868966076 + 0.5714285715 u = 0.868966076 + 0.5714285715 Combine like terms: 0.868966076 + 0.5714285715 = 1.4403946475 u = 1.4403946475 Simplifying u = 1.4403946475Subproblem 2
u + -0.5714285715 = -0.868966076 Simplifying u + -0.5714285715 = -0.868966076 Reorder the terms: -0.5714285715 + u = -0.868966076 Solving -0.5714285715 + u = -0.868966076 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + u = -0.868966076 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + u = -0.868966076 + 0.5714285715 u = -0.868966076 + 0.5714285715 Combine like terms: -0.868966076 + 0.5714285715 = -0.2975375045 u = -0.2975375045 Simplifying u = -0.2975375045Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.4403946475, -0.2975375045}
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